Pernicious numbers: Difference between revisions
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888888877 888888878 888888880 888888883 888888885 888888886 |
888888877 888888878 888888880 888888883 888888885 888888886 |
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</pre> |
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=={{header|Ksh}}== |
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<lang ksh> |
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#!/bin/ksh |
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# Positive integer whose population count is a prime |
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# # Variables: |
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# |
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integer PNUM=25 MINN=888888877 MAXN=888888888 |
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# # Functions: |
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# |
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# # Function _dec2bin(n) - return binary representation of decimal n |
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# |
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function _dec2bin { |
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typeset _n ; integer _n=$1 |
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typeset _base ; integer _base=2 |
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typeset _q _r _buff ; integer _q _r |
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typeset -a _arr _barr |
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(( _q = _n / _base )) |
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(( _r = _n % _base )) |
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_arr+=( ${_r} ) |
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until (( _q == 0 )); do |
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_n=${_q} |
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(( _q = _n / _base )) |
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(( _r = _n % _base )) |
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_arr+=( ${_r} ) |
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done |
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_revarr _arr _barr |
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_buff=${_barr[@]} |
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echo ${_buff// /} |
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} |
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# # Function _revarr(arr, barr) - reverse arr into barr |
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# |
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function _revarr { |
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typeset _arr ; nameref _arr="$1" |
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typeset _barr ; nameref _barr="$2" |
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typeset _i ; integer _i |
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for ((_i=${#_arr[*]}-1; _i>=0; _i--)); do |
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_barr+=( ${_arr[_i]} ) |
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done |
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} |
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# # Function _isprime(n) return 1 for prime, 0 for not prime |
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# |
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function _isprime { |
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typeset _n ; integer _n=$1 |
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typeset _i ; integer _i |
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(( _n < 2 )) && return 0 |
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for (( _i=2 ; _i*_i<=_n ; _i++ )); do |
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(( ! ( _n % _i ) )) && return 0 |
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done |
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return 1 |
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} |
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# # Function _sumdigits(n) return sum of n's digits |
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# |
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function _sumdigits { |
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typeset _n ; _n=$1 |
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typeset _i _sum ; integer _i _sum=0 |
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for ((_i=0; _i<${#_n}; _i++)); do |
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(( _sum+=${_n:${_i}:1} )) |
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done |
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echo ${_sum} |
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} |
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###### |
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# main # |
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###### |
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integer i sbi n=3 cnt=0 |
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printf "First $PNUM Pernicious numbers:\n" |
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for ((n = cnt = 0; cnt < PNUM; n++)); do |
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bi=$(_dec2bin ${n}) # $n as Binary |
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sbi=${bi//0/} # Strip zeros (i.e. count ones) |
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_isprime ${#sbi} # One count prime? |
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(( $? )) && { printf "%4d " ${n} ; ((++cnt)) } |
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done |
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printf "\n\nPernicious numbers between %11,d and %11,d inclusive:\n" $MINN $MAXN |
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for ((i=MINN; i<=MAXN; i++)); do |
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bi=$(_dec2bin ${i}) |
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sbi=${bi//0/} |
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_isprime ${#sbi} |
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(( $? )) && printf "%12,d " ${i} |
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done |
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echo |
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</lang> |
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{{out}}<pre> |
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First 25 Pernicious numbers: |
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3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 |
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Pernicious numbers between 888,888,877 and 888,888,888 inclusive: |
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888,888,877 888,888,878 888,888,880 888,888,883 888,888,885 888,888,886 |
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</pre> |
</pre> |
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Revision as of 18:54, 25 December 2021
You are encouraged to solve this task according to the task description, using any language you may know.
A pernicious number is a positive integer whose population count is a prime.
The population count is the number of ones in the binary representation of a non-negative integer.
- Example
22 (which is 10110 in binary) has a population count of 3, which is prime, and therefore
22 is a pernicious number.
- Task
- display the first 25 pernicious numbers (in decimal).
- display all pernicious numbers between 888,888,877 and 888,888,888 (inclusive).
- display each list of integers on one line (which may or may not include a title).
- See also
- Sequence A052294 pernicious numbers on The On-Line Encyclopedia of Integer Sequences.
- Rosetta Code entry population count, evil numbers, odious numbers.
11l
<lang 11l>F popcount(n)
R bin(n).count(‘1’)
F is_prime(n)
I n < 2
R 0B
L(i) 2 .. Int(sqrt(n))
I n % i == 0
R 0B
R 1B
V i = 0 V cnt = 0 L
I is_prime(popcount(i))
print(i, end' ‘ ’)
cnt++
I cnt == 25
L.break
i++
print() L(i) 888888877..888888888
I is_prime(popcount(i))
print(i, end' ‘ ’)</lang>
- Output:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886
360 Assembly
For maximum compatibility, this program uses only the basic instruction set (S/360) with 2 ASSIST macros (XDECO,XPRNT). <lang 360asm>* Pernicious numbers 04/05/2016 PERNIC CSECT
USING PERNIC,R13 base register and savearea pointer
SAVEAREA B STM-SAVEAREA(R15)
DC 17F'0'
STM STM R14,R12,12(R13) save registers
ST R13,4(R15) link backward SA
ST R15,8(R13) link forward SA
LR R13,R15 establish addressability
SR R7,R7 n=0
MVC PG,=CL80' ' clear buffer
LA R10,PG pgi
LA R6,1 i=1
LOOPI1 C R7,=F'25' do i=1 while(n<25)
BNL ELOOPI1
LR R1,R6 i
BAL R14,POPCOUNT
LR R1,R0 popcount(i)
BAL R14,ISPRIME
C R0,=F'1' if isprime(popcount(i))=1
BNE NOTPRIM1
XDECO R6,XDEC edit i
MVC 0(3,R10),XDEC+9 output i format I3
LA R10,3(R10) pgi=pgi+3
LA R7,1(R7) n=n+1
NOTPRIM1 LA R6,1(R6) i=i+1
B LOOPI1
ELOOPI1 XPRNT PG,80 print buffer
MVC PG,=CL80' ' clear buffer
LA R10,PG pgi
L R6,=F'888888877' i=888888877
LOOPI2 C R6,=F'888888888' do i to 888888888
BH ELOOPI2
LR R1,R6 i
BAL R14,POPCOUNT
LR R1,R0 popcount(i)
BAL R14,ISPRIME
C R0,=F'1' if isprime(popcount(i))=1
BNE NOTPRIM2
XDECO R6,XDEC edit i
MVC 0(10,R10),XDEC+2 output i format I10
LA R10,10(R10) pgi=pgi+10
NOTPRIM2 LA R6,1(R6) i=i+1
B LOOPI2
ELOOPI2 XPRNT PG,80 print buffer
L R13,4(0,R13) restore savearea pointer
LM R14,R12,12(R13) restore registers
XR R15,R15 return code = 0
BR R14 -------------- end main
POPCOUNT CNOP 0,4 -------------- popcount(xx) [R8,R11]
ST R14,POPCOUSA save return address
ST R1,XX store argument
SR R11,R11 rr=0
SR R8,R8 ii=0
LOOPII C R8,=F'31' do ii=0 to 31
BH ELOOPII
L R1,XX xx
LR R2,R8 ii
BAL R14,BTEST
C R0,=F'1' if btest(xx,ii)=1
BNE NOTBTEST
LA R11,1(R11) rr=rr+1
NOTBTEST LA R8,1(R8) ii=ii+1
B LOOPII
ELOOPII LR R0,R11 return(rr)
L R14,POPCOUSA
BR R14 -------------- end popcount
ISPRIME CNOP 0,4 -------------- isprime(number) [R9]
ST R14,ISPRIMSA save return address
ST R1,NUMBER store argument
C R1,=F'2' if number=2
BNE ELSE1
MVC ISPRIMEX,=F'1' isprimex=1
B ELOOPJJ
ELSE1 L R1,NUMBER
C R1,=F'2' if number<2
BL EVEN
L R4,NUMBER
SRDA R4,32
D R4,=F'2' mod(number,2)
C R4,=F'0' if mod(number,2)=0
BNE ELSE2
EVEN MVC ISPRIMEX,=F'0' isprimex=0
B ELOOPJJ
ELSE2 MVC ISPRIMEX,=F'1' isprimex=1
LA R9,3 jj=3
LOOPJJ LR R5,R9 jj
MR R4,R9 jj*jj
C R5,NUMBER do jj=3 by 1 while jj*jj<=number
BH ELOOPJJ
L R4,NUMBER
SRDA R4,32
DR R4,R9 mod(number,jj)
LTR R4,R4 if mod(number,jj)=0
BNZ ITERJJ
MVC ISPRIMEX,=F'0' isprimex=0
L R0,ISPRIMEX return(isprimex)
B ISPRIMRT
ITERJJ LA R9,1(R9) jj=jj+1
B LOOPJJ
ELOOPJJ L R0,ISPRIMEX return(isprimex) ISPRIMRT L R14,ISPRIMSA
BR R14 -------------- end isprime
BTEST CNOP 0,4 -------------- btest(word,n) [R0:R3]
LA R0,1 ok=1; return(1) if word(n)='1'b
LR R3,R2 i=n
LOOPB LTR R3,R3 if i=0
BZ ELOOPB
SRL R1,1 Shift Right Logical
BCTR R3,0 i=i-1
B LOOPB
ELOOPB STC R1,BTESTX x=word
TM BTESTX,B'00000001' if bit(word,n)='1'b
BO BTESTRET
LA R0,0 ok=0; return(0) if word(n)='0'b
BTESTRET BR R14 -------------- end btest XX DS F paramter of popcount NUMBER DS F paramter of isprime ISPRIMEX DS F return value of isprime BTESTX DS X byte to see in btest POPCOUSA DS A return address of popcount ISPRIMSA DS A return address of isprime PG DS CL80 buffer XDEC DS CL12 edit zone
YREGS
END PERNIC</lang>
- Output:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886
Ada
Uses package Population_Count from Population count#Ada.
<lang Ada>with Ada.Text_IO, Population_Count; use Population_Count;
procedure Pernicious is
Prime: array(0 .. 64) of Boolean;
-- we are using 64-bit numbers, so the population count is between 0 and 64
X: Num; use type Num;
Cnt: Positive;
begin
-- initialize array Prime; Prime(I) must be true if and only if I is a prime
Prime := (0 => False, 1 => False, others => True);
for I in 2 .. 8 loop
if Prime(I) then
Cnt := I + I; while Cnt <= 64 loop Prime(Cnt) := False; Cnt := Cnt + I; end loop;
end if;
end loop;
-- print first 25 pernicious numbers
X := 1;
for I in 1 .. 25 loop
while not Prime(Pop_Count(X)) loop
X := X + 1;
end loop;
Ada.Text_IO.Put(Num'Image(X));
X := X + 1;
end loop;
Ada.Text_IO.New_Line;
-- print pernicious numbers between 888_888_877 and 888_888_888 (inclusive)
for Y in Num(888_888_877) .. 888_888_888 loop
if Prime(Pop_Count(Y)) then
Ada.Text_IO.Put(Num'Image(Y));
end if; end loop; Ada.Text_IO.New_Line;
end;</lang>
- Output:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886
A small modification allows to count all the pernicious numbers between 1 and 2**32 in about 32 seconds:
<lang Ada> Counter: Natural; begin
-- initialize array Prime; Prime(I) must be true if and only if I is a prime ...
Counter := 0;
-- count p. numbers below 2**32
for Y in Num(2) .. 2**32 loop
if Prime(Pop_Count(Y)) then
Counter := Counter + 1;
end if; end loop; Ada.Text_IO.Put_Line(Natural'Image(Counter));
end Count_Pernicious;</lang>
- Output:
> time ./count_pernicious 1421120880 real 0m33.375s user 0m33.372s sys 0m0.000s
ALGOL 68
<lang algol68># calculate various pernicious numbers #
- returns the population (number of bits on) of the non-negative integer n #
PROC population = ( INT n )INT:
BEGIN
INT number := n;
INT result := 0;
WHILE number > 0 DO
IF ODD number THEN result +:= 1 FI;
number OVERAB 2
OD;
result
END # population # ;
- as we are dealing with 32 bit numbers, the maximum possible population is 32 #
- so we only need a table of whether the integers 0 : 32 are prime or not #
- we use the sieve of Eratosthenes... #
INT max number = 32; [ 0 : max number ]BOOL is prime; is prime[ 0 ] := FALSE; is prime[ 1 ] := FALSE; FOR i FROM 2 TO max number DO is prime[ i ] := TRUE OD; FOR i FROM 2 TO ENTIER sqrt( max number ) DO
IF is prime[ i ] THEN FOR p FROM i * i BY i TO max number DO is prime[ p ] := FALSE OD FI
OD;
- returns TRUE if n is pernicious, FALSE otherwise #
PROC is pernicious = ( INT n )BOOL: is prime[ population( n ) ];
- find the first 25 pernicious numbers, 0 and 1 are not pernicious #
INT pernicious count := 0; FOR i FROM 2 WHILE pernicious count < 25 DO
IF is pernicious( i ) THEN
# found a pernicious number #
print( ( whole( i, 0 ), " " ) );
pernicious count +:= 1
FI
OD; print( ( newline ) );
- find the pernicious numbers between 888 888 877 and 888 888 888 #
FOR i FROM 888 888 877 TO 888 888 888 DO
IF is pernicious( i ) THEN
print( ( whole( i, 0 ), " " ) )
FI
OD; print( ( newline ) ) </lang>
- Output:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886
ALGOL W
<lang algolw>begin % find some pernicious numbers: numbers with a prime population count %
% returns the population count of n %
integer procedure populationCount( integer value n ) ;
begin
integer v, count;
count := 0;
v := abs n;
while v > 0 do begin
if odd( v ) then count := count + 1;
v := v div 2
end while_v_gt_0 ;
count
end populationCount ;
% sets p( 1 :: n ) to a sieve of primes up to n %
procedure Eratosthenes ( logical array p( * ) ; integer value n ) ;
begin
p( 1 ) := false; p( 2 ) := true;
for i := 3 step 2 until n do p( i ) := true;
for i := 4 step 2 until n do p( i ) := false;
for i := 3 step 2 until truncate( sqrt( n ) ) do begin
integer ii; ii := i + i;
if p( i ) then for pr := i * i step ii until n do p( pr ) := false
end for_i ;
end Eratosthenes ;
% returns true if p is pernicious, false otherwise, s must be a sieve %
% of primes upto 32 %
logical procedure isPernicious ( integer value p; logical array s ( * ) ) ; p > 0 and s( populationCount( p ) );
% find the pernicious numbers %
begin
% as we are dealing with 32 bit numbers, the maximum possible %
% population is 32 %
logical array isPrime ( 1 :: 32 );
integer p, pCount;
Eratosthenes( isPrime, 32 );
% show the first 25 pernicious numbers %
pCount := 0;
p := 2; % 0 and 1 aren't pernicious, so start at 2 %
while pCount < 25 do begin
if isPernicious( p, isPrime ) then begin
% have a pernicious number %
pCount := pCount + 1;
writeon( i_w := 1, s_w := 0, " ", p )
end if_pernicious_p ;
p := P + 1
end for_p ;
write();
% find the pernicious numbers between 888 888 877 and 888 888 888 %
for p := 888888877 until 888888888 do begin
if isPernicious( p, isPrime ) then writeon( i_w := 1, s_w := 0, " ", p )
end for_p ;
write();
end
end.</lang>
- Output:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886
AppleScript
<lang applescript>on isPrime(n)
if (n < 4) then return (n > 1)
if ((n mod 2 is 0) or (n mod 3 is 0)) then return false
repeat with i from 5 to (n ^ 0.5) div 1 by 6
if ((n mod i is 0) or (n mod (i + 2) is 0)) then return false
end repeat
return true
end isPrime
on isPernicious(n)
-- 8 bits at a time is statistically slightly more efficient than 1 bit at a time.
set popCount to (n mod 4 + 1) div 2 + (n mod 16 + 4) div 8
set n to n div 16
repeat until (n = 0)
set popCount to popCount + (n mod 4 + 1) div 2 + (n mod 16 + 4) div 8
set n to n div 16
end repeat
return isPrime(popCount)
end isPernicious
-- Task code: on intToText(n)
set output to ""
repeat until (n < 100000000)
set output to text 2 thru 9 of ((100000000 + (n mod 100000000 as integer)) as text) & output
set n to n div 100000000
end repeat
set output to (n as integer as text) & output
return output
end intToText
on join(lst, delim)
set astid to AppleScript's text item delimiters set AppleScript's text item delimiters to delim set output to lst as text set AppleScript's text item delimiters to astid return output
end join
on task()
set l1 to {}
set n to 0
set counter to 0
repeat until (counter = 25)
if (isPernicious(n)) then
set end of l1 to n
set counter to counter + 1
end if
set n to n + 1
end repeat
set l2 to {}
-- One solution to 8,888,877 and up being too large to be AppleScript repeat indices.
repeat with i from 88888877 to 88888888
set n to 8.0E+8 + i
if (isPernicious(n)) then set end of l2 to intToText(n)
end repeat
return join(l1, " ") & (linefeed & join(l2, " "))
end task
task()</lang>
- Output:
<lang applescript>"3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886"</lang>
Arturo
<lang rebol>pernicious?: function [n][
prime? size filter split as.binary n 'x -> x="0"
]
i: 1 found: 0 while [found<25][
if pernicious? i [
prints i
prints " "
found: found + 1
]
i: i + 1
] print "" print select 888888877..888888888 => pernicious?</lang>
- Output:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886
AutoHotkey
<lang AutoHotkey>c := 0 while c < 25 if IsPern(A_Index) Out1 .= A_Index " ", c++ Loop, 12 if IsPern(n := 888888876 + A_Index) Out2 .= n " " MsgBox, % Out1 "`n" Out2
IsPern(x) { ;https://en.wikipedia.org/wiki/Hamming_weight#Efficient_implementation static p := {2:1, 3:1, 5:1, 7:1, 11:1, 13:1, 17:1, 19:1, 23:1, 29:1, 31:1, 37:1, 41:1, 43:1, 47:1, 53:1, 59:1, 61:1} x -= (x >> 1) & 0x5555555555555555 , x := (x & 0x3333333333333333) + ((x >> 2) & 0x3333333333333333) , x := (x + (x >> 4)) & 0x0f0f0f0f0f0f0f0f return p[(x * 0x0101010101010101) >> 56] }</lang>
- Output:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886
AWK
<lang AWK>
- syntax: GAWK -f PERNICIOUS_NUMBERS.AWK
BEGIN {
pernicious(25) pernicious(888888877,888888888) exit(0)
} function pernicious(x,y, count,n) {
if (y == "") { # print first X pernicious numbers
while (count < x) {
if (is_prime(pop_count(++n)) == 1) {
printf("%d ",n)
count++
}
}
}
else { # print pernicious numbers in X-Y range
for (n=x; n<=y; n++) {
if (is_prime(pop_count(n)) == 1) {
printf("%d ",n)
}
}
}
print("")
} function dec2bin(n, str) {
while (n) {
if (n%2 == 0) {
str = "0" str
}
else {
str = "1" str
}
n = int(n/2)
}
if (str == "") {
str = "0"
}
return(str)
} function is_prime(x, i) {
if (x <= 1) {
return(0)
}
for (i=2; i<=int(sqrt(x)); i++) {
if (x % i == 0) {
return(0)
}
}
return(1)
} function pop_count(n) {
n = dec2bin(n) return gsub(/1/,"&",n)
} </lang>
- Output:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886
Befunge
Based more or less on the C implementation, although we don't bother supporting n = 0, so we can use a smaller prime bit set that fits inside a signed 32 bit int (most Befunge implementations wouldn't support anything higher).
Also note that the extra spaces in the output are just to ensure it's readable on buggy interpreters that don't include a space after numeric output. They can easily be removed by replacing the comma on line 3 with a dollar.
<lang befunge>55*00p1>:"ZOA>/"***7-*>\:2>/\v >8**`!#^_$@\<(^v^)>/#2^#\<2 2 ^+**"X^yYo":+1<_:.48*,00v|: <% v".D}Tx"$,+55_^#!p00:-1g<v |< > * + : * * + ^^ ! % 2 $ <^ <^</lang>
- Output:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886
C
<lang c>#include <stdio.h>
typedef unsigned uint; uint is_pern(uint n) {
uint c = 2693408940u; // int with all prime-th bits set
while (n) c >>= 1, n &= (n - 1); // take out lowerest set bit one by one
return c & 1;
}
int main(void) {
uint i, c;
for (i = c = 0; c < 25; i++)
if (is_pern(i))
printf("%u ", i), ++c;
putchar('\n');
for (i = 888888877u; i <= 888888888u; i++)
if (is_pern(i))
printf("%u ", i);
putchar('\n');
return 0;
}</lang>
- Output:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886
C#
<lang csharp>using System; using System.Linq;
namespace PerniciousNumbers {
class Program
{
public static int PopulationCount(long n)
{
int cnt = 0;
do
{
if ((n & 1) != 0)
{
cnt++;
}
} while ((n >>= 1) > 0);
return cnt;
}
public static bool isPrime(int x)
{
if (x <= 2 || (x & 1) == 0)
{
return x == 2;
}
var limit = Math.Sqrt(x);
for (int i = 3; i <= limit; i += 2)
{
if (x % i == 0)
{
return false;
}
}
return true;
}
private static IEnumerable<int> Pernicious(int start, int count, int take)
{
return Enumerable.Range(start, count).Where(n => isPrime(PopulationCount(n))).Take(take);
}
static void Main(string[] args)
{
foreach (var n in Pernicious(0, int.MaxValue, 25))
{
Console.Write("{0} ", n);
}
Console.WriteLine();
foreach (var n in Pernicious(888888877, 11, 11))
{
Console.Write("{0} ", n);
}
Console.ReadKey();
}
}
}</lang>
- Output:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886
C++
<lang cpp>
- include <iostream>
using namespace std;
int main() {
int cnt = 0, cnt2, cnt3, tmp, binary[8];
for (int i = 3; cnt < 25; i++) {
tmp = i;
cnt2 = 0;
cnt3 = 0;
for (int j = 7; j > 0; j--) {
binary[j] = tmp % 2;
tmp /= 2;
}
binary[0] = tmp;
for (int j = 0; j < 8; j++) {
if (binary[j] == 1) {
cnt2++;
}
}
for (int j = 2; j <= (cnt2 / 2); j++) {
if (cnt2 % j == 0) {
cnt3++;
break;
}
}
if (cnt3 == 0 && cnt2 != 1) {
cout << i << endl;
cnt++;
}
}
cout << endl; int binary2[31];
for (int i = 888888877; i <= 888888888; i++) {
tmp = i;
cnt2 = 0;
cnt3 = 0;
for (int j = 30; j > 0; j--) {
binary2[j] = tmp % 2;
tmp /= 2;
}
binary2[0] = tmp;
for (int j = 0; j < 31; j++) {
if (binary2[j] == 1) {
cnt2++;
}
}
for (int j = 2; j <= (cnt2 / 2); j++) {
if (cnt2 % j == 0) {
cnt3++;
break;
}
}
if (cnt3 == 0 && cnt2 != 1) {
cout << i << endl;
}
}
} </lang>
- Output:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886
Clojure
<lang clojure>(defn counting-numbers
([] (counting-numbers 1)) ([n] (lazy-seq (cons n (counting-numbers (inc n))))))
(defn divisors [n] (filter #(zero? (mod n %)) (range 1 (inc n)))) (defn prime? [n] (= (divisors n) (list 1 n))) (defn pernicious? [n]
(prime? (count (filter #(= % \1) (Integer/toString n 2)))))
(println (take 25 (filter pernicious? (counting-numbers)))) (println (filter pernicious? (range 888888877 888888889)))</lang>
- Output:
(3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36) (888888877 888888878 888888880 888888883 888888885 888888886)
CLU
<lang clu>% The population count of an integer is never going to be % higher than the amount of bits in it (max 64) % so we can get away with a very simple primality test. is_prime = proc (n: int) returns (bool)
if n<=2 then return(n=2) end
if n//2=0 then return(false) end
for i: int in int$from_to_by(n+2, n/2, 2) do
if n//i=0 then return(false) end
end
return(true)
end is_prime
% Find the population count of a number pop_count = proc (n: int) returns (int)
c: int := 0
while n > 0 do
c := c + n // 2
n := n / 2
end
return(c)
end pop_count
% Is N pernicious? pernicious = proc (n: int) returns (bool)
return(is_prime(pop_count(n)))
end pernicious
start_up = proc ()
po: stream := stream$primary_output()
stream$putl(po, "First 25 pernicious numbers: ")
n: int := 1
seen: int := 0
while seen<25 do
if pernicious(n) then
stream$puts(po, int$unparse(n) || " ")
seen := seen + 1
end
n := n + 1
end
stream$putl(po, "\nPernicious numbers between 888,888,877 and 888,888,888:")
for i: int in int$from_to(888888877,888888888) do
if pernicious(i) then
stream$puts(po, int$unparse(i) || " ")
end
end
end start_up</lang>
- Output:
First 25 pernicious numbers: 3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 Pernicious numbers between 888,888,877 and 888,888,888: 888888877 888888878 888888880 888888883 888888885 888888886
Common Lisp
Using primep from Primality by trial division task.
<lang lisp>(format T "~{~a ~}~%"
(loop for n = 1 then (1+ n)
when (primep (logcount n))
collect n into numbers
when (= (length numbers) 25)
return numbers))
(format T "~{~a ~}~%"
(loop for n from 888888877 to 888888888
when (primep (logcount n))
collect n))</lang>
- Output:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886
D
<lang d>void main() {
import std.stdio, std.algorithm, std.range, core.bitop;
immutable pernicious = (in uint n) => (2 ^^ n.popcnt) & 0xA08A28AC; uint.max.iota.filter!pernicious.take(25).writeln; iota(888_888_877, 888_888_889).filter!pernicious.writeln;
}</lang>
- Output:
[3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 31, 33, 34, 35, 36] [888888877, 888888878, 888888880, 888888883, 888888885, 888888886]
Where 0xA08A28AC == 0b_1010_0000__1000_1010__0010_1000__1010_1100, that is a bit set equivalent to the prime numbers [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31] of the range (0, 31].
This high-level code is fast enough to allow to count all the 1_421_120_880 Pernicious numbers in the unsigned 32 bit range in less than 48 seconds with this line: <lang d>uint.max.iota.filter!pernicious.walkLength.writeln;</lang>
EchoLisp
<lang scheme> (lib 'sequences)
(define (pernicious? n) (prime? (bit-count n)))
(define pernicious (filter pernicious? [1 .. ])) (take pernicious 25)
→ (3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36)
(take (filter pernicious? [888888877 .. 888888889]) #:all)
→ (888888877 888888878 888888880 888888883 888888885 888888886)
</lang>
Eiffel
<lang Eiffel> class APPLICATION
create make
feature
make -- Test of is_pernicious_number. local test: LINKED_LIST [INTEGER] i: INTEGER do create test.make from i := 1 until test.count = 25 loop if is_pernicious_number (i) then test.extend (i) end i := i + 1 end across test as t loop io.put_string (t.item.out + " ") end io.new_line across 888888877 |..| 888888888 as c loop if is_pernicious_number (c.item) then io.put_string (c.item.out + " ") end end end
is_pernicious_number (n: INTEGER): BOOLEAN -- Is 'n' a pernicious_number? require positiv_input: n > 0 do Result := is_prime (count_population (n)) end
feature{NONE}
count_population (n: INTEGER): INTEGER -- Population count of 'n'. require positiv_input: n > 0 local j: INTEGER math: DOUBLE_MATH do create math j := math.log_2 (n).ceiling + 1 across 0 |..| j as c loop if n.bit_test (c.item) then Result := Result + 1 end end end
is_prime (n: INTEGER): BOOLEAN --Is 'n' a prime number? require positiv_input: n > 0 local i: INTEGER max: REAL_64 math: DOUBLE_MATH do create math if n = 2 then Result := True elseif n <= 1 or n \\ 2 = 0 then Result := False else Result := True max := math.sqrt (n) from i := 3 until i > max loop if n \\ i = 0 then Result := False end i := i + 2 end end end
end </lang>
- Output:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886
Elixir
<lang Elixir> defmodule SieveofEratosthenes do
def init(lim) do find_primes(2,lim,(2..lim)) end
def find_primes(count,lim,nums) when (count * count) > lim do nums end
def find_primes(count,lim,nums) when (count * count) <= lim do e = Enum.reject(nums,&(rem(&1,count) == 0 and &1 > count)) find_primes(count+1,lim,e) end
end
defmodule PerniciousNumbers do
def take(n) do
primes = SieveofEratosthenes.init(100)
Stream.iterate(1,&(&1+1))
|> Stream.filter(&(pernicious?(&1,primes)))
|> Enum.take(n)
|> IO.inspect
end
def between(a..b) do
primes = SieveofEratosthenes.init(100)
a..b
|> Stream.filter(&(pernicious?(&1,primes)))
|> Enum.to_list
|> IO.inspect
end
def ones(num) do
num
|> Integer.to_string(2)
|> String.codepoints
|> Enum.count(fn n -> n == "1" end)
end
def pernicious?(n,primes), do: Enum.member?(primes,ones(n))
end </lang>
<lang Elixir> PerniciousNumbers.take(25) PerniciousNumbers.between(888_888_877..888_888_888) </lang>
- Output:
[3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 31, 33, 34, 35, 36]
[888888877, 888888878, 888888880, 888888883, 888888885, 888888886]
F#
<lang fsharp>open System
//Taken from https://gist.github.com/rmunn/bc49d32a586cdfa5bcab1c3e7b45d7ac let bitcount (n : int) =
let count2 = n - ((n >>> 1) &&& 0x55555555) let count4 = (count2 &&& 0x33333333) + ((count2 >>> 2) &&& 0x33333333) let count8 = (count4 + (count4 >>> 4)) &&& 0x0f0f0f0f (count8 * 0x01010101) >>> 24
//Modified from other examples to actually state the 1 is not prime let isPrime n =
if n < 2 then
false
else
let sqrtn n = int <| sqrt (float n)
seq { 2 .. sqrtn n } |> Seq.exists(fun i -> n % i = 0) |> not
[<EntryPoint>] let main _ =
[1 .. 100] |> Seq.filter (bitcount >> isPrime) |> Seq.take 25 |> Seq.toList |> printfn "%A" [888888877 .. 888888888] |> Seq.filter (bitcount >> isPrime) |> Seq.toList |> printfn "%A" 0 // return an integer exit code</lang>
- Output:
[3; 5; 6; 7; 9; 10; 11; 12; 13; 14; 17; 18; 19; 20; 21; 22; 24; 25; 26; 28; 31; 33; 34; 35; 36] [888888877; 888888878; 888888880; 888888883; 888888885; 888888886]
Factor
<lang factor>USING: lists lists.lazy math.bitwise math.primes math.ranges prettyprint sequences ;
- pernicious? ( n -- ? ) bit-count prime? ;
25 0 lfrom [ pernicious? ] lfilter ltake list>array . ! print first 25 pernicious numbers 888,888,877 888,888,888 [a,b] [ pernicious? ] filter . ! print pernicious numbers in range</lang>
- Output:
{ 3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 }
{ 888888877 888888878 888888880 888888883 888888885 888888886 }
Forth
<lang forth>: popcount { n -- u }
0 begin n 0<> while n n 1- and to n 1+ repeat ;
\ primality test for 0 <= n <= 63
- prime? ( n -- ? )
1 swap lshift 0x28208a20a08a28ac and 0<> ;
- pernicious? ( n -- ? )
popcount prime? ;
- first_n_pernicious_numbers { n -- }
." First " n . ." pernicious numbers:" cr
1
begin
n 0 >
while
dup pernicious? if
dup .
n 1- to n
then
1+
repeat
drop cr ;
- pernicious_numbers_between { m n -- }
." Pernicious numbers between " m . ." and " n 1 .r ." :" cr n 1+ m do i pernicious? if i . then loop cr ;
25 first_n_pernicious_numbers 888888877 888888888 pernicious_numbers_between
bye</lang>
- Output:
First 25 pernicious numbers: 3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 Pernicious numbers between 888888877 and 888888888: 888888877 888888878 888888880 888888883 888888885 888888886
Fortran
<lang fortran>program pernicious
implicit none
integer :: i, n
i = 1
n = 0
do
if(isprime(popcnt(i))) then
write(*, "(i0, 1x)", advance = "no") i
n = n + 1
if(n == 25) exit
end if
i = i + 1
end do
write(*,*)
do i = 888888877, 888888888
if(isprime(popcnt(i))) write(*, "(i0, 1x)", advance = "no") i
end do
contains
function popcnt(x)
integer :: popcnt integer, intent(in) :: x integer :: i popcnt = 0 do i = 0, 31 if(btest(x, i)) popcnt = popcnt + 1 end do
end function
function isprime(number)
logical :: isprime
integer, intent(in) :: number
integer :: i
if(number == 2) then
isprime = .true.
else if(number < 2 .or. mod(number,2) == 0) then
isprime = .false.
else
isprime = .true.
do i = 3, int(sqrt(real(number))), 2
if(mod(number,i) == 0) then
isprime = .false.
exit
end if
end do
end if
end function end program</lang>
- Output:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886
FreeBASIC
<lang freebasic> ' FreeBASIC v1.05.0 win64
Function SumBinaryDigits(number As Integer) As Integer
If number < 0 Then number = -number ' convert negative numbers to positive Var sum = 0 While number > 0 sum += number Mod 2 number \= 2 Wend Return sum
End Function
Function IsPrime(number As Integer) As Boolean
If number <= 1 Then
Return false
ElseIf number <= 3 Then
Return true
ElseIf number Mod 2 = 0 OrElse number Mod 3 = 0 Then
Return false
End If
Var i = 5
While i * i <= number
If number Mod i = 0 OrElse number Mod (i + 2) = 0 Then
Return false
End If
i += 6
Wend
Return True
End Function
Function IsPernicious(number As Integer) As Boolean
Dim popCount As Integer = SumBinaryDigits(number) Return IsPrime(popCount)
End Function
Dim As Integer n = 1, count = 0 Print "The following are the first 25 pernicious numbers :" Print
Do
If IsPernicious(n) Then Print Using "###"; n; count += 1 End If n += 1
Loop Until count = 25
Print : Print Print "The pernicious numbers between 888,888,877 and 888,888,888 inclusive are :" Print For n = 888888877 To 888888888
If IsPernicious(n) Then Print Using "##########"; n;
Next Print : Print Print "Press any key to exit the program" Sleep End </lang>
- Output:
The following are the first 25 pernicious numbers : 3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 The pernicious numbers between 888,888,877 and 888,888,888 inclusive are : 888888877 888888878 888888880 888888883 888888885 888888886
Fōrmulæ
Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition.
Programs in Fōrmulæ are created/edited online in its website, However they run on execution servers. By default remote servers are used, but they are limited in memory and processing power, since they are intended for demonstration and casual use. A local server can be downloaded and installed, it has no limitations (it runs in your own computer). Because of that, example programs can be fully visualized and edited, but some of them will not run if they require a moderate or heavy computation/memory resources, and no local server is being used.
In this page you can see the program(s) related to this task and their results.
Go
<lang go>package main
import "fmt"
func pernicious(w uint32) bool {
const (
ff = 1<<32 - 1
mask1 = ff / 3
mask3 = ff / 5
maskf = ff / 17
maskp = ff / 255
)
w -= w >> 1 & mask1
w = w&mask3 + w>>2&mask3
w = (w + w>>4) & maskf
return 0xa08a28ac>>(w*maskp>>24)&1 != 0
}
func main() {
for i, n := 0, uint32(1); i < 25; n++ {
if pernicious(n) {
fmt.Printf("%d ", n)
i++
}
}
fmt.Println()
for n := uint32(888888877); n <= 888888888; n++ {
if pernicious(n) {
fmt.Printf("%d ", n)
}
}
fmt.Println()
}</lang>
- Output:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886
Groovy
<lang Groovy> class example{ static void main(String[] args){ def n=0; def counter=0; while(counter<25){ if(print(n)){ counter++;} n=n+1; } println(); def x=888888877; while(x<888888889){ print(x); x++;} } static def print(def a){ def primes=[2,3,5,7,11,13,17,19,23,29,31,37,41,43,47]; def c=Integer.toBinaryString(a); String d=c; def e=0; for(i in d){if(i=='1'){e++;}} if(e in primes){printf(a+" ");return 1;} } } </lang>
- Output:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886
Haskell
<lang Haskell>module Pernicious
where
isPernicious :: Integer -> Bool isPernicious num = isPrime $ toInteger $ length $ filter ( == 1 ) $ toBinary num
isPrime :: Integer -> Bool isPrime number = divisors number == [1, number]
where
divisors :: Integer -> [Integer]
divisors number = [ m | m <- [1 .. number] , number `mod` m == 0 ]
toBinary :: Integer -> [Integer] toBinary num = reverse $ map ( `mod` 2 ) ( takeWhile ( /= 0 ) $ iterate ( `div` 2 ) num )
solution1 = take 25 $ filter isPernicious [1 ..] solution2 = filter isPernicious [888888877 .. 888888888]</lang>
- Output:
[3,5,6,7,9,10,11,12,13,14,17,18,19,20,21,22,24,25,26,28,31,33,34,35,36] [888888877,888888878,888888880,888888883,888888885,888888886]
Or, in a point-free and applicative style, using unfoldr for the population count:
<lang Haskell>import Data.Numbers.Primes (isPrime) import Data.List (unfoldr) import Data.Tuple (swap) import Data.Bool (bool)
isPernicious :: Int -> Bool isPernicious = isPrime . popCount
popCount :: Int -> Int popCount =
sum . unfoldr ((flip bool Nothing . Just . swap . flip quotRem 2) <*> (0 ==))
main :: IO () main =
mapM_ print [ take 25 $ filter isPernicious [1 ..] , filter isPernicious [888888877 .. 888888888] ]</lang>
- Output:
[3,5,6,7,9,10,11,12,13,14,17,18,19,20,21,22,24,25,26,28,31,33,34,35,36] [888888877,888888878,888888880,888888883,888888885,888888886]
Icon and Unicon
Works in both languages: <lang unicon>link "factors"
procedure main(A)
every writes((pernicious(seq())\25||" ") | "\n") every writes((pernicious(888888877 to 888888888)||" ") | "\n")
end
procedure pernicious(n)
return (isprime(c1bits(n)),n)
end
procedure c1bits(n)
c := 0 while n > 0 do c +:= 1(n%2, n/:=2) return c
end</lang>
- Output:
->pn 3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886 ->
J
Implementation:
<lang J>ispernicious=: 1 p: +/"1@#:</lang>
Task (thru taken from the Loops/Downward for task).:
<lang J> 25{.I.ispernicious i.100 3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
thru=: <. + i.@(+*)@-~ 888888877 + I. ispernicious 888888877 thru 888888888
888888877 888888878 888888880 888888883 888888885 888888886</lang>
Java
<lang java>public class Pernicious{
//very simple isPrime since x will be <= Long.SIZE
public static boolean isPrime(int x){
if(x < 2) return false;
for(int i = 2; i < x; i++){
if(x % i == 0) return false;
}
return true;
}
public static int popCount(long x){
return Long.bitCount(x);
}
public static void main(String[] args){
for(long i = 1, n = 0; n < 25; i++){
if(isPrime(popCount(i))){
System.out.print(i + " ");
n++;
}
}
System.out.println();
for(long i = 888888877; i <= 888888888; i++){
if(isPrime(popCount(i))) System.out.print(i + " ");
}
}
}</lang>
- Output:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886
jq
The most interesting detail in the following is perhaps the use of recurse/1 to define the helper function bin, which generates the binary bits. <lang jq># is_prime is designed to work with jq 1.4 def is_prime:
if . == 2 then true
else 2 < . and . % 2 == 1 and
. as $in
| (($in + 1) | sqrt) as $m
| (((($m - 1) / 2) | floor) + 1) as $max
| reduce range(1; $max) as $i
(true; if . then ($in % ((2 * $i) + 1)) > 0 else false end)
end;
def popcount:
def bin: recurse( if . == 0 then empty else ./2 | floor end ) % 2; [bin] | add;
def is_pernicious: popcount | is_prime;
- Emit a stream of "count" pernicious numbers greater than
- or equal to m:
def pernicious(m; count):
if count > 0 then
if m | is_pernicious then m, pernicious(m+1; count -1)
else pernicious(m+1; count)
end
else empty
end;
def task:
# display the first 25 pernicious numbers: [ pernicious(1;25) ],
# display all pernicious numbers between # 888,888,877 and 888,888,888 (inclusive). [ range(888888877; 888888889) | select( is_pernicious ) ]
task</lang>
- Output:
[3,5,6,7,9,10,11,12,13,14,17,18,19,20,21,22,24,25,26,28,31,33,34,35,36] [888888877,888888878,888888880,888888883,888888885,888888886]
Julia
<lang julia>using Primes
ispernicious(n::Integer) = isprime(count_ones(n)) nextpernicious(n::Integer) = begin n += 1; while !ispernicious(n) n += 1 end; return n end function perniciouses(n::Int)
rst = Vector{Int}(n)
rst[1] = 3
for i in 2:n
rst[i] = nextpernicious(rst[i-1])
end
return rst
end perniciouses(a::Integer, b::Integer) = filter(ispernicious, a:b)
println("First 25 pernicious numbers: ", join(perniciouses(25), ", ")) println("Perniciouses in [888888877, 888888888]: ", join(perniciouses(888888877, 888888888), ", ")) </lang>
- Output:
First 25 pernicious numbers: 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 31, 33, 34, 35, 36 Perniciouses in [888888877, 888888888]: 888888877, 888888878, 888888880, 888888883, 888888885, 888888886
Kotlin
<lang scala>// version 1.0.5-2
fun isPrime(n: Int): Boolean {
if (n < 2) return false
if (n % 2 == 0) return n == 2
if (n % 3 == 0) return n == 3
var d : Int = 5
while (d * d <= n) {
if (n % d == 0) return false
d += 2
if (n % d == 0) return false
d += 4
}
return true
}
fun getPopulationCount(n: Int): Int {
if (n <= 0) return 0
var nn = n
var sum = 0
while (nn > 0) {
sum += nn % 2
nn /= 2
}
return sum
}
fun isPernicious(n: Int): Boolean = isPrime(getPopulationCount(n))
fun main(args: Array<String>) {
var n = 1
var count = 0
println("The first 25 pernicious numbers are:\n")
do {
if (isPernicious(n)) {
print("$n ")
count++
}
n++
}
while (count < 25)
println("\n")
println("The pernicious numbers between 888,888,877 and 888,888,888 inclusive are:\n")
for (i in 888888877..888888888) {
if (isPernicious(i)) print("$i ")
}
}</lang>
- Output:
The first 25 pernicious numbers are: 3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 The pernicious numbers between 888,888,877 and 888,888,888 inclusive are: 888888877 888888878 888888880 888888883 888888885 888888886
Ksh
<lang ksh>
- !/bin/ksh
- Positive integer whose population count is a prime
- # Variables:
integer PNUM=25 MINN=888888877 MAXN=888888888
- # Functions:
- # Function _dec2bin(n) - return binary representation of decimal n
function _dec2bin { typeset _n ; integer _n=$1 typeset _base ; integer _base=2 typeset _q _r _buff ; integer _q _r typeset -a _arr _barr
(( _q = _n / _base )) (( _r = _n % _base )) _arr+=( ${_r} ) until (( _q == 0 )); do _n=${_q} (( _q = _n / _base )) (( _r = _n % _base )) _arr+=( ${_r} ) done _revarr _arr _barr _buff=${_barr[@]} echo ${_buff// /} }
- # Function _revarr(arr, barr) - reverse arr into barr
function _revarr { typeset _arr ; nameref _arr="$1" typeset _barr ; nameref _barr="$2" typeset _i ; integer _i
for ((_i=${#_arr[*]}-1; _i>=0; _i--)); do _barr+=( ${_arr[_i]} ) done }
- # Function _isprime(n) return 1 for prime, 0 for not prime
function _isprime { typeset _n ; integer _n=$1 typeset _i ; integer _i
(( _n < 2 )) && return 0 for (( _i=2 ; _i*_i<=_n ; _i++ )); do (( ! ( _n % _i ) )) && return 0 done return 1 }
- # Function _sumdigits(n) return sum of n's digits
function _sumdigits { typeset _n ; _n=$1 typeset _i _sum ; integer _i _sum=0
for ((_i=0; _i<${#_n}; _i++)); do (( _sum+=${_n:${_i}:1} )) done echo ${_sum} }
######
- main #
######
integer i sbi n=3 cnt=0
printf "First $PNUM Pernicious numbers:\n" for ((n = cnt = 0; cnt < PNUM; n++)); do bi=$(_dec2bin ${n}) # $n as Binary sbi=${bi//0/} # Strip zeros (i.e. count ones) _isprime ${#sbi} # One count prime? (( $? )) && { printf "%4d " ${n} ; ((++cnt)) } done
printf "\n\nPernicious numbers between %11,d and %11,d inclusive:\n" $MINN $MAXN for ((i=MINN; i<=MAXN; i++)); do bi=$(_dec2bin ${i}) sbi=${bi//0/} _isprime ${#sbi} (( $? )) && printf "%12,d " ${i} done echo </lang>
- Output:
First 25 Pernicious numbers:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36Pernicious numbers between 888,888,877 and 888,888,888 inclusive:
888,888,877 888,888,878 888,888,880 888,888,883 888,888,885 888,888,886
Lua
<lang Lua>-- Test primality by trial division function isPrime (x)
if x < 2 then return false end
if x < 4 then return true end
if x % 2 == 0 then return false end
for d = 3, math.sqrt(x), 2 do
if x % d == 0 then return false end
end
return true
end
-- Take decimal number, return binary string function dec2bin (n)
local bin, bit = ""
while n > 0 do
bit = n % 2
n = math.floor(n / 2)
bin = bit .. bin
end
return bin
end
-- Take decimal number, return population count as number function popCount (n)
local bin, count = dec2bin(n), 0
for pos = 1, bin:len() do
if bin:sub(pos, pos) == "1" then count = count + 1 end
end
return count
end
-- Print pernicious numbers in range if two arguments provided, or function pernicious (x, y) -- the first 'x' if only one argument.
if y then
for n = x, y do
if isPrime(popCount(n)) then io.write(n .. " ") end
end
else
local n, count = 0, 0
while count < x do
if isPrime(popCount(n)) then
io.write(n .. " ")
count = count + 1
end
n = n + 1
end
end
print()
end
-- Main procedure pernicious(25) pernicious(888888877, 888888888)</lang>
- Output:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886
Maple
<lang Maple>ispernicious := proc(n::posint)
return evalb(isprime(rhs(Statistics:-Tally(StringTools:-Explode(convert(convert(n, binary), string)))[-1])));
end proc;
print_pernicious := proc(n::posint) local k, count, list_num; count := 0; list_num := []; for k while count < n do
if ispernicious(k) then
count := count + 1;
list_num := [op(list_num), k];
end if;
end do; return list_num; end proc:
range_pernicious := proc(n::posint, m::posint) local k, list_num; list_num := []; for k from n to m do
if ispernicious(k) then
list_num := [op(list_num), k];
end if;
end do; return list_num; end proc:</lang>
- Output:
[3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 31, 33, 34, 35, 36] [888888877, 888888878, 888888880, 888888883, 888888885, 888888886]
Mathematica/Wolfram Language
<lang Mathematica>popcount[n_Integer] := IntegerDigits[n, 2] // Total perniciousQ[n_Integer] := popcount[n] // PrimeQ perniciouscount = 0; perniciouslist = {}; i = 0; While[perniciouscount < 25,
If[perniciousQ[i], AppendTo[perniciouslist, i]; perniciouscount++]; i++]
Print["first 25 pernicious numbers"] perniciouslist (*******) perniciouslist2 = {}; Do[
If[perniciousQ[i], AppendTo[perniciouslist2, i]]
, {i, 888888877, 888888888}]
Print["Pernicious numbers between 888,888,877 and 888,888,888 (inclusive)"] perniciouslist2</lang>
- Output:
first 25 pernicious numbers
{3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 31, 33, 34, 35, 36}
Pernicious numbers between 888,888,877 and 888,888,888 (inclusive)
{888888877, 888888878, 888888880, 888888883, 888888885, 888888886}
Alternate Code
test function <lang Mathematica>perniciousQ[n_Integer] := PrimeQ@Total@IntegerDigits[n, 2]</lang> First 25 pernicious numbers <lang Mathematica>n = 0; NestWhile[Flatten@{#, If[perniciousQ[++n], n, {}]} &, {}, Length@# < 25 &]</lang> Pernicious numbers betweeen 888888877 and 888888888 inclusive <lang Mathematica>Cases[Range[888888877, 888888888], _?(perniciousQ@# &)]</lang>
Modula-2
<lang modula2>MODULE Pernicious; FROM FormatString IMPORT FormatString; FROM Terminal IMPORT WriteString,WriteLn,ReadChar;
PROCEDURE IsPrime(x : LONGINT) : BOOLEAN; VAR i : LONGINT; BEGIN
IF x<2 THEN RETURN FALSE END;
FOR i:=2 TO x-1 DO
IF x MOD i = 0 THEN RETURN FALSE END
END;
RETURN TRUE
END IsPrime;
PROCEDURE BitCount(x : LONGINT) : LONGINT; VAR count : LONGINT; BEGIN
count := 0;
WHILE x>0 DO
x := x BAND (x-1);
INC(count)
END;
RETURN count
END BitCount;
VAR
buf : ARRAY[0..63] OF CHAR; i,n : LONGINT;
BEGIN
i := 1;
n := 0;
WHILE n<25 DO
IF IsPrime(BitCount(i)) THEN
FormatString("%l ", buf, i);
WriteString(buf);
INC(n)
END;
INC(i)
END;
WriteLn;
FOR i:=888888877 TO 888888888 DO
IF IsPrime(BitCount(i)) THEN
FormatString("%l ", buf, i);
WriteString(buf)
END;
END;
ReadChar
END Pernicious.</lang>
Nim
<lang nim>import strutils
proc count(s: string; sub: char): int =
var i = 0
while true:
i = s.find(sub, i)
if i < 0:
break
inc i
inc result
proc popcount(n: int): int = n.toBin(64).count('1')
const primes = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61}
var p: seq[int] var i = 0 while p.len < 25:
if popcount(i) in primes: p.add i inc i
echo p
p = @[] i = 888_888_877 while i <= 888_888_888:
if popcount(i) in primes: p.add i inc i
echo p</lang>
- Output:
@[3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 31, 33, 34, 35, 36] @[888888877, 888888878, 888888880, 888888883, 888888885, 888888886]
Panda
<lang panda>fun prime(a) type integer->integer
a where countTemplate:A.factor==2
fun pernisc(a) type integer->integer
a where sumTemplate:A.radix:2 .char.integer.integer.prime
1..36.pernisc 888888877..888888888.pernisc</lang>
- Output:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886
PARI/GP
<lang parigp>pern(n)=isprime(hammingweight(n)) select(pern, [1..36]) select(pern,[888888877..888888888])</lang>
- Output:
%1 = [3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 31, 33, 34, 35, 36] %2 = [888888877, 888888878, 888888880, 888888883, 888888885, 888888886]
Pascal
Inspired by Ada, using array of primes to simply add.An if-then takes to long.
Added easy counting of pernicious numbers for full Bit ranges like 32-Bit <lang pascal>program pernicious; {$IFDEF FPC}
{$OPTIMIZATION ON,Regvar,ASMCSE,CSE,PEEPHOLE}// 3x speed up
{$ENDIF} uses
sysutils;//only used for time
type
tbArr = array[0..64] of byte;
{
PrimeTil64 : array[0..64] of byte = (0,0,2,3,0,5,0, 7,0,0,0,11,0,13,0,0,0,17,0,19,0,0,0,23,0,0,0,0,0,29,0, 31,0,0,0,0,0,37,0,0,0,41,0,43,0,0,0,47,0, 0,0,0,0,53,0,0,0,0,0,59,0, 61,0,0,0);
} const
PrimeTil64 : tbArr =
(0,0,1,1,0,1,0, 1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,
1,0,0,0,0,0, 1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,
1,0,0,0);
function n_beyond_k(n,k: NativeInt):Uint64; var
i : NativeInt;
Begin
result := 1; IF 2*k>= n then k := n-k; For i := 1 to k do Begin result := result *n DIV i; dec(n); end;
end;
function popcnt32(n:Uint32):NativeUint; //https://en.wikipedia.org/wiki/Hamming_weight#Efficient_implementation const
K1 = $0101010101010101; K33 = $3333333333333333; K55 = $5555555555555555; KF1 = $0F0F0F0F0F0F0F0F;
begin
n := n- (n shr 1) AND NativeUint(K55); n := (n AND NativeUint(K33))+ ((n shr 2) AND NativeUint(K33)); n := (n + (n shr 4)) AND NativeUint(KF1); n := (n*NativeUint(K1)) SHR 24; popcnt32 := n;
end;
var
bit1cnt, k : LongWord; PernCnt : Uint64;
Begin
writeln('the 25 first pernicious numbers');
k:=1;
PernCnt:=0;
repeat
IF PrimeTil64[popCnt32(k)] <> 0 then Begin
inc(PernCnt); write(k,' ');end;
inc(k);
until PernCnt >= 25;
writeln;
writeln('pernicious numbers in [888888877..888888888]');
For k := 888888877 to 888888888 do
IF PrimeTil64[popCnt32(k)] <> 0 then
write(k,' ');
writeln(#13#10);
k := 8;
repeat
PernCnt := 0;
For bit1cnt := 0 to k do
Begin
//i == number of Bits set,n_beyond_k(k,i) == number of arrangements
IF PrimeTil64[bit1cnt] <> 0 then
inc(PernCnt,n_beyond_k(k,bit1cnt));
end;
writeln(PernCnt,' pernicious numbers in [0..2^',k,'-1]');
inc(k,k);
until k>64;
end.</lang>
- Output:
the 25 first pernicious numbers 3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 pernicious numbers in [888888877..888888888] 888888877 888888878 888888880 888888883 888888885 888888886 148 pernicious numbers in [0..2^8-1] 21416 pernicious numbers in [0..2^16-1] 1421120880 pernicious numbers in [0..2^32-1] 1214766910143514374 pernicious numbers in [0..2^64-1]
Perl
<lang perl>sub is_pernicious {
my $n = shift;
my $c = 2693408940; # primes < 32 as set bits
while ($n) { $c >>= 1; $n &= ($n - 1); }
$c & 1;
}
my ($i, @p) = 0; while (@p < 25) {
push @p, $i if is_pernicious($i); $i++;
}
print join ' ', @p; print "\n"; ($i, @p) = (888888877,); while ($i < 888888888) {
push @p, $i if is_pernicious($i); $i++;
}
print join ' ', @p;</lang>
- Output:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886
Alternately, generating the same output using a method similar to Pari/GP:
<lang perl>use ntheory qw/is_prime hammingweight/; my $i = 1; my @pern = map { $i++ while !is_prime(hammingweight($i)); $i++; } 1..25; print "@pern\n"; print join(" ", grep { is_prime(hammingweight($_)) } 888888877 .. 888888888), "\n";</lang>
Phix
<lang Phix>function pernicious(integer n)
return is_prime(sum(int_to_bits(n,32)))
end function
sequence s = {} integer n = 1 while length(s)<25 do
if pernicious(n) then
s &= n
end if
n += 1
end while ?s s = {} for i=888_888_877 to 888_888_888 do
if pernicious(i) then
s &= i
end if
end for ?s</lang>
- Output:
{3,5,6,7,9,10,11,12,13,14,17,18,19,20,21,22,24,25,26,28,31,33,34,35,36}
{888888877,888888878,888888880,888888883,888888885,888888886}
PicoLisp
Using 'prime?' from Primality by trial division#PicoLisp. <lang PicoLisp>(de pernicious? (N)
(prime? (cnt = (chop (bin N)) '("1" .))) )</lang>
Test: <lang PicoLisp>: (let N 0
(do 25
(until (pernicious? (inc 'N)))
(printsp N) ) )
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 -> 36
- (filter pernicious? (range 888888877 888888888))
-> (888888877 888888878 888888880 888888883 888888885 888888886)</lang>
PL/I
<lang PL/I> pern: procedure options (main);
declare (i, n) fixed binary (31);
n = 3;
do i = 1 to 25, 888888877 to 888888888;
if i = 888888877 then do; n = i ; put skip; end;
do while ( ^is_prime ( tally(bit(n), '1'b) ) );
n = n + 1;
end;
put edit( trim(n), ' ') (a);
n = n + 1;
end;
is_prime: procedure (n) returns (bit(1));
declare n fixed (15); declare i fixed (10);
if n < 2 then return ('0'b);
if n = 2 then return ('1'b);
if mod(n, 2) = 0 then return ('0'b);
do i = 3 to sqrt(n) by 2;
if mod(n, i) = 0 then return ('0'b);
end;
return ('1'b);
end is_prime;
end pern; </lang> Results:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886 888888889 888888890 888888892 888888897 888888898 888888900
Plain English
<lang plainenglish>To decide if a number is pernicious: Find a population count of the number. If the population count is prime, say yes. Say no.
To find a population count of a number: Privatize the number. Loop. If the number is 0, exit. Bitwise and the number with the number minus 1. Bump the population count. Repeat.
To run: Start up. Show the first twenty-five pernicious numbers. Show the pernicious numbers between 888888877 and 888888888. Wait for the escape key. Shut down.
To show the first twenty-five pernicious numbers: Put 0 into a number. Put 0 into a pernicious number count. Loop. If the pernicious number count is greater than 24, write "" on the console; exit. If the number is pernicious, show the number; bump the pernicious number count. Bump the number. Repeat.
To show a number: Convert the number to a string. Write the string then " " on the console without advancing.
To show the pernicious numbers between a number and another number: Privatize the number. Subtract 1 from the number. Loop. If the number is past the other number, exit. If the number is pernicious, show the number. Repeat.</lang>
- Output:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886
PowerShell
<lang PowerShell> function pop-count($n) {
(([Convert]::ToString($n, 2)).toCharArray() | where {$_ -eq '1'}).count
}
function isPrime ($n) {
if ($n -eq 1) {$false}
elseif ($n -eq 2) {$true}
elseif ($n -eq 3) {$true}
else{
$m = [Math]::Floor([Math]::Sqrt($n))
(@(2..$m | where {($_ -lt $n) -and ($n % $_ -eq 0) }).Count -eq 0)
}
}
$i = 0 $num = 1 $arr = while($i -lt 25) {
if((isPrime (pop-count $num))) {
$i++
$num
}
$num++
} "first 25 pernicious numbers" "$arr" "" "pernicious numbers between 888,888,877 and 888,888,888" "$(888888877..888888888 | where{isprime(pop-count $_)})" </lang> Output:
First 25 pernicious numbers 3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 Pernicious numbers between 888,888,877 and 888,888,888 888888877 888888878 888888880 888888883 888888885 888888886
As An Advanced Function
Just an exercise in how to make the input more "PowerShelly".
The PopCount property is available in each of the returned integers. <lang PowerShell> function Select-PerniciousNumber {
[CmdletBinding()]
[OutputType([int])]
Param
(
[Parameter(Mandatory=$true,
ValueFromPipeline=$true,
ValueFromPipelineByPropertyName=$true,
Position=0)]
$InputObject
)
Begin
{
function Test-Prime ([int]$n)
{
$n = [Math]::Abs($n)
if ($n -eq 0 -or $n -eq 1) {return $false}
for ($m = 2; $m -le [Math]::Sqrt($n); $m++)
{
if (($n % $m) -eq 0) {return $false}
}
return $true
}
[scriptblock]$popCount = {(([Convert]::ToString($this, 2)).ToCharArray() | Where-Object {$_ -eq '1'}).Count}
}
Process
{
foreach ($object in $InputObject)
{
$object | Add-Member -MemberType ScriptProperty -Name PopCount -Value $popCount -Force -PassThru | ForEach-Object {
if (Test-Prime $_.PopCount)
{
$_
}
}
}
}
} </lang> <lang PowerShell> $start, $end = 0, 999999 $range1 = $start..$end | Select-PerniciousNumber | Select-Object -First 25
"First {0} pernicious numbers:`n{1}`n" -f $range1.Count, ($range1 -join ", ")
$start, $end = 888888877, 888888888 $range2 = $start..$end | Select-PerniciousNumber
"Pernicious numbers between {0} and {1}:`n{2}`n" -f $start, $end, ($range2 -join ", ") </lang>
- Output:
First 25 pernicious numbers: 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 31, 33, 34, 35, 36 Pernicious numbers between 888888877 and 888888888: 888888877, 888888878, 888888880, 888888883, 888888885, 888888886
PureBasic
<lang PureBasic> EnableExplicit
Procedure.i SumBinaryDigits(Number)
If Number < 0 : number = -number : EndIf; convert negative numbers to positive Protected sum = 0 While Number > 0 sum + Number % 2 Number / 2 Wend ProcedureReturn sum
EndProcedure
Procedure.i IsPrime(Number)
If Number <= 1
ProcedureReturn #False
ElseIf Number <= 3
ProcedureReturn #True
ElseIf Number % 2 = 0 Or Number % 3 = 0
ProcedureReturn #False
EndIf
Protected i = 5
While i * i <= Number
If Number % i = 0 Or Number % (i + 2) = 0
ProcedureReturn #False
EndIf
i + 6
Wend
ProcedureReturn #True
EndProcedure
Procedure.i IsPernicious(Number)
Protected popCount = SumBinaryDigits(Number) ProcedureReturn Bool(IsPrime(popCount))
EndProcedure
Define n = 1, count = 0 If OpenConsole()
PrintN("The following are the first 25 pernicious numbers :")
PrintN("")
Repeat
If IsPernicious(n)
Print(RSet(Str(n), 3))
count + 1
EndIf
n + 1
Until count = 25
PrintN("")
PrintN("")
PrintN("The pernicious numbers between 888,888,877 and 888,888,888 inclusive are : ")
PrintN("")
For n = 888888877 To 888888888
If IsPernicious(n)
Print(RSet(Str(n), 10))
EndIf
Next
PrintN("")
PrintN("")
PrintN("Press any key to close the console")
Repeat: Delay(10) : Until Inkey() <> ""
CloseConsole()
EndIf </lang>
- Output:
The following are the first 25 pernicious numbers : 3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 The pernicious numbers between 888,888,877 and 888,888,888 inclusive are : 888888877 888888878 888888880 888888883 888888885 888888886
Python
Procedural
<lang python>>>> def popcount(n): return bin(n).count("1")
>>> primes = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61} >>> p, i = [], 0 >>> while len(p) < 25:
if popcount(i) in primes: p.append(i)
i += 1
>>> p
[3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 31, 33, 34, 35, 36]
>>> p, i = [], 888888877
>>> while i <= 888888888:
if popcount(i) in primes: p.append(i)
i += 1
>>> p
[888888877, 888888878, 888888880, 888888883, 888888885, 888888886]
>>> </lang>
Functional
<lang python>Pernicious numbers
from itertools import count, islice
- isPernicious :: Int -> Bool
def isPernicious(n):
True if the population count of n is
a prime number.
return isPrime(popCount(n))
- oeisA052294 :: [Int]
def oeisA052294():
A non-finite stream of pernicious numbers.
(Numbers with a prime population count)
return (x for x in count(1) if isPernicious(x))
- popCount :: Int -> Int
def popCount(n):
The count of non-zero digits in the binary
representation of the positive integer n.
def go(x):
return divmod(x, 2) if 0 < x else None
return sum(unfoldl(go)(n))
- ------------------------- TEST -------------------------
- main :: IO ()
def main():
First 25, and any in the range
[888,888,877..888,888,888]
print(
take(25)(
oeisA052294()
)
)
print([
x for x in enumFromTo(888888877)(888888888)
if isPernicious(x)
])
- ----------------------- GENERIC ------------------------
- enumFromTo :: Int -> Int -> [Int]
def enumFromTo(m):
Enumeration of integer values [m..n]
def go(n):
return range(m, 1 + n)
return go
- isPrime :: Int -> Bool
def isPrime(n):
True if n is prime.
if n in (2, 3):
return True
if 2 > n or 0 == n % 2:
return False
if 9 > n:
return True
if 0 == n % 3:
return False
return not any(map(
lambda x: 0 == n % x or 0 == n % (2 + x),
range(5, 1 + int(n ** 0.5), 6)
))
- take :: Int -> [a] -> [a]
- take :: Int -> String -> String
def take(n):
The prefix of xs of length n,
or xs itself if n > length xs.
return lambda xs: (
xs[0:n]
if isinstance(xs, (list, tuple))
else list(islice(xs, n))
)
- unfoldl :: (b -> Maybe (b, a)) -> b -> [a]
def unfoldl(f):
A lazy (generator) list unfolded from a seed value
by repeated application of f until no residue remains.
Dual to fold/reduce.
f returns either None or just (residue, value).
For a strict output list, wrap the result with list()
def go(v):
residueValue = f(v)
while residueValue:
yield residueValue[1]
residueValue = f(residueValue[0])
return go
- MAIN ---
if __name__ == '__main__':
main()</lang>
- Output:
[3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 31, 33, 34, 35, 36] [888888877, 888888878, 888888880, 888888883, 888888885, 888888886]
Quackery
<lang Quackery> [ $ "rosetta/seive.qky" loadfile
$ "rosetta/popcount.qky" loadfile ] now!
( i.e. using the code at ) ( http://rosettacode.org/wiki/Sieve_of_Eratosthenes and ) ( http://rosettacode.org/wiki/Population_count )
29 eratosthenes ( Precompute as many primes as are required )
( for the task. 888,888,888 is a 30 bit )
( number less than (2^30)-1 so primes up to )
( 29 will suffice. )
[ 1+ over - times
[ dup i^ +
dup popcount
isprime iff
[ echo sp ]
else drop ]
drop ] is perniciousrange ( n n --> )
25 echopopwith isprime cr 888888877 888888888 perniciousrange cr</lang>
- Output:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886
Racket
<lang racket>#lang racket (require math/number-theory rnrs/arithmetic/bitwise-6)
(define pernicious? (compose prime? bitwise-bit-count))
(define (dnl . strs)
(for-each displayln strs))
(define (show-sequence seq)
(string-join (for/list ((v (in-values*-sequence seq))) (~a ((if (list? v) car values) v))) ", "))
(dnl
"Task requirements:" "display the first 25 pernicious numbers." (show-sequence (in-parallel (sequence-filter pernicious? (in-naturals 1)) (in-range 25))) "display all pernicious numbers between 888,888,877 and 888,888,888 (inclusive)." (show-sequence (sequence-filter pernicious? (in-range 888888877 (add1 888888888)))))
(module+ test
(require rackunit) (check-true (pernicious? 22)))</lang>
- Output:
Task requirements: display the first 25 pernicious numbers. 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 31, 33, 34, 35, 36 display all pernicious numbers between 888,888,877 and 888,888,888 (inclusive). 888888877, 888888878, 888888880, 888888883, 888888885, 888888886
Raku
(formerly Perl 6)
Straightforward implementation using Raku's is-prime built-in subroutine. <lang perl6>sub is-pernicious(Int $n --> Bool) {
is-prime [+] $n.base(2).comb;
}
say (grep &is-pernicious, 0 .. *)[^25]; say grep &is-pernicious, 888_888_877 .. 888_888_888;</lang>
- Output:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886
REXX
Programming note: to increase the size of the numbers being tested (to greater than 100 decimal digits),
all that is needed is to extend the list of low primes in the 2nd line in the pernicious procedure (below);
the highest prime (Hprime) should exceed the number of decimal digits in 2Hprime.
The program could be easily extended by programmatically generating enough primes to handle much larger numbers.
╔════════════════════════════════════════════════════════════════════════════════════════╗ ╠═════ How the ─── popCount ─── function works (working from the inner─most level): ═════╣ ║ ║ ║ arg(1) obtains the value of the 1st argument passed to the (popCount) function. ║ ║ d2x converts a decimal string ──► heXadecimal (it may have a leading zeroes).║ ║ +0 adds zero to the (above) string, removing any superfluous leading zeroes. ║ ║ translate converts all zeroes to blanks (the 2nd argument defaults to a blank). ║ ║ space removes all blanks from the character string (now only containing '1's). ║ ║ length counts the number of characters in the string. ║ ║ return returns the above value to the invoker. ║ ║ ║ ║ Note that all values in REXX are stored as (eight─bit) characters. ║ ╚════════════════════════════════════════════════════════════════════════════════════════╝
<lang rexx>/*REXX program computes and displays a number (and also a range) of pernicious numbers.*/ numeric digits 100 /*be able to handle large numbers. */ parse arg N L H . /*obtain optional arguments from the CL*/ if N== | N==',' then N=25 /*N not given? Then use the default. */ if L== | L==',' then L=888888877 /*L " " " " " " */ if H== | H==',' then H=888888888 /*H " " " " " " */ say 'The 1st ' N " pernicious numbers are:" /*display a nice title for the numbers.*/ say pernicious(1,,N) /*get all pernicious # from 1 ─~─► N. */ say /*display a blank line for a separator.*/ say 'Pernicious numbers between ' L " and " H ' (inclusive) are:' say pernicious(L,H) /*get all pernicious # from L ───► H. */ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ pernicious: procedure; parse arg bot,top,lim /*obtain the bot and top numbers, limit*/
p='2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101'
@.=0
do k=1 until _== /*examine the list of some low primes.*/
_=word(p, k); @._=1 /*generate an array " " " " */
end /*k*/
$= /*list of pernicious numbers (so far). */
if m== then m=999999999 /*Not given? Then use a gihugic limit.*/
if top== then top=999999999 /* " " " " " " " */
#=0 /*number of pernicious numbers (so far)*/
do j=bot to top until #==lim /*generate pernicious #s 'til satisfied*/
pc=popCount(j) /*obtain the population count for J. */
if \@.pc then iterate /*if popCount not in @.prime, skip it.*/
$=$ j /*append a pernicious number to list. */
#=#+1 /*bump the pernicious number count. */
end /*j*/
return substr($, 2) /*return the results, sans 1st blank. */
/*──────────────────────────────────────────────────────────────────────────────────────*/ popCount: return length( space( translate( x2b( d2x(arg(1))) +0,, 0), 0)) /*count 1's.*/</lang> output when the default inputs are used:
The 1st 25 pernicious numbers are: 3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 Pernicious numbers between 888888877 and 888888888 (inclusive) are: 888888877 888888878 888888880 888888883 888888885 888888886
Ring
Programming note: as written, this program can't handle the large numbers required for the 2nd task requirement (it receives a Numeric Overflow). <lang ring>
- Project : Pernicious numbers
see "The first 25 pernicious numbers:" + nl nr = 0 for n=1 to 50
sum = 0
str = decimaltobase(n, 2)
for m=1 to len(str)
if str[m] = "1"
sum = sum + 1
ok
next
if isprime(sum)
nr = nr + 1
see "" + n + " "
ok
if nr = 25
exit
ok
next
func decimaltobase(nr, base)
binary = 0
i = 1
while(nr != 0)
remainder = nr % base
nr = floor(nr/base)
binary= binary + (remainder*i)
i = i*10
end
return string(binary)
func isprime num
if (num <= 1) return 0 ok
if (num % 2 = 0 and num != 2) return 0 ok
for i = 3 to floor(num / 2) -1 step 2
if (num % i = 0) return 0 ok
next
return 1
</lang> Output:
The first 25 pernicious numbers: 3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
Ruby
<lang ruby>require "prime"
class Integer
def popcount
to_s(2).count("1") #Ruby 2.4: digits(2).count(1)
end
def pernicious?
popcount.prime?
end
end
p 1.step.lazy.select(&:pernicious?).take(25).to_a p ( 888888877..888888888).select(&:pernicious?)</lang>
- Output:
[3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 31, 33, 34, 35, 36] [888888877, 888888878, 888888880, 888888883, 888888885, 888888886]
Rust
<lang rust> extern crate aks_test_for_primes;
use std::iter::Filter; use std::ops::RangeFrom;
use aks_test_for_primes::is_prime;
fn main() {
for i in pernicious().take(25) {
print!("{} ", i);
}
println!();
for i in (888_888_877u64..888_888_888).filter(is_pernicious) {
print!("{} ", i);
}
}
fn pernicious() -> Filter<RangeFrom<u64>, fn(&u64) -> bool> {
(0u64..).filter(is_pernicious as fn(&u64) -> bool)
}
fn is_pernicious(n: &u64) -> bool {
is_prime(n.count_ones())
} </lang>
- Output:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886
S-lang
<lang S-lang>% Simplistic prime-test from prime-by-trial-division: define is_prime(n) {
if (n <= 1) return(0); if (n == 2) return(1); if ((n & 1) == 0) return(0);
variable mx = int(sqrt(n)), i;
_for i (3, mx, 1) {
if ((n mod i) == 0)
return(0);
}
return(1);
}
define population(n) {
variable pc = 0;
do {
if (n & 1) pc++;
n /= 2;
}
while (n);
return(pc);
}
define is_pernicious(n) {
return(is_prime(population(n)));
}
variable plist = {}, n = 0; while (length(plist) < 25) {
n++;
if (is_pernicious(n))
list_append(plist, string(n));
} print(strjoin(list_to_array(plist), " "));
plist = {}; _for n (888888877, 888888888, 1) {
if (is_pernicious(n))
list_append(plist, string(n));
} print(strjoin(list_to_array(plist), " ")); </lang>
- Output:
"3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36"
- Output:
"888888877 888888878 888888880 888888883 888888885 888888886"
Scala
<lang scala>def isPernicious( v:Long ) : Boolean = BigInt(v.toBinaryString.toList.filter( _ == '1' ).length).isProbablePrime(16)
// Generate the output {
val (a,b1,b2) = (25,888888877L,888888888L)
println( Stream.from(2).filter( isPernicious(_) ).take(a).toList.mkString(",") )
println( {for( i <- b1 to b2 if( isPernicious(i) ) ) yield i}.mkString(",") )
}</lang>
- Output:
3,5,6,7,9,10,11,12,13,14,17,18,19,20,21,22,24,25,26,28,31,33,34,35,36 888888877,888888878,888888880,888888883,888888885,888888886
Seed7
The function popcount below converts
the integer into a bitset.
The function card
is used to compute the population count of the bitset.
<lang seed7>$ include "seed7_05.s7i";
const set of integer: primes is {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61};
const func integer: popcount (in integer: number) is
return card(bitset(number));
const proc: main is func
local
var integer: num is 0;
var integer: count is 0;
begin
for num range 0 to integer.last until count >= 25 do
if popcount(num) in primes then
write(num <& " ");
incr(count);
end if;
end for;
writeln;
for num range 888888877 to 888888888 do
if popcount(num) in primes then
write(num <& " ");
end if;
end for;
writeln;
end func;</lang>
- Output:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886
Sidef
<lang ruby>func is_pernicious(n) {
n.sumdigits(2).is_prime
}
say is_pernicious.first(25).join(' ') say is_pernicious.grep(888_888_877..888_888_888).join(' ')</lang>
- Output:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886
Swift
<lang swift>import Foundation
extension BinaryInteger {
@inlinable
public var isPrime: Bool {
if self == 0 || self == 1 {
return false
} else if self == 2 {
return true
}
let max = Self(ceil((Double(self).squareRoot())))
for i in stride(from: 2, through: max, by: 1) where self % i == 0 {
return false
}
return true }
}
public func populationCount(n: Int) -> Int {
guard n >= 0 else {
return 0
}
return String(n, radix: 2).lazy.filter({ $0 == "1" }).count
}
let first25 = (1...).lazy.filter({ populationCount(n: $0).isPrime }).prefix(25) let rng = (888_888_877...888_888_888).lazy.filter({ populationCount(n: $0).isPrime })
print("First 25 Pernicious numbers: \(Array(first25))") print("Pernicious numbers between 888_888_877...888_888_888: \(Array(rng))")</lang>
- Output:
First 25 Pernicious numbers: [3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 31, 33, 34, 35, 36] Pernicious numbers between 888_888_877...888_888_888: [888888877, 888888878, 888888880, 888888883, 888888885, 888888886]
Symsyn
<lang symsyn>
primes : 0b0010100000100000100010100010000010100000100010100010100010101100
| the first 25 pernicious numbers
$T | clear string
num_pn | set to zero
2 n | start at 2
5 hi_bit
if num_pn LT 25
call popcount | count ones
if primes bit pop_cnt | if pop_cnt bit of bit vector primes is one
+ num_pn | inc number of pernicious numbers
~ n $S | convert to decimal string
+ ' ' $S | pad a space
+ $S $T | add to string $T
endif
+ pop_cnt | next number (odd) has one more bit than previous (even)
+ n | next number
if primes bit pop_cnt
+ num_pn
~ n $S
+ ' ' $S
+ $S $T
endif
+ n
goif | go back to if
endif
$T [] | display numbers
| pernicious numbers in range 888888877 .. 888888888
$T | clear string
num_pn | set to zero
888888876 n | start at 888888876
29 hi_bit
if n LE 888888888
call popcount | count ones
if primes bit pop_cnt | if pop_cnt bit of bit vector primes is one
+ num_pn | inc number of pernicious numbers
~ n $S | convert to decimal string
+ ' ' $S | pad a space
+ $S $T | add to string $T
endif
+ pop_cnt | next number (odd) has one more bit than previous (even)
+ n | next number
if primes bit pop_cnt
+ num_pn
~ n $S
+ ' ' $S
+ $S $T
endif
+ n
goif | go back to if
endif
$T [] | display numbers
stop
popcount | count ones in bit field
pop_cnt | pop_cnt to zero
1 bit_num | only count even numbers so skip bit 0
if bit_num LE hi_bit
if n bit bit_num
+ pop_cnt
endif
+ bit_num
goif
endif
return
</lang>
- Output:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 37 888888877 888888878 888888880 888888883 888888885 888888886 888888889
Tcl
<lang tcl>package require math::numtheory
proc pernicious {n} {
::math::numtheory::isprime [tcl::mathop::+ {*}[split [format %b $n] ""]]
}
for {set n 0;set p {}} {[llength $p] < 25} {incr n} {
if {[pernicious $n]} {lappend p $n}
} puts [join $p ","] for {set n 888888877; set p {}} {$n <= 888888888} {incr n} {
if {[pernicious $n]} {lappend p $n}
} puts [join $p ","]</lang>
- Output:
3,5,6,7,9,10,11,12,13,14,17,18,19,20,21,22,24,25,26,28,31,33,34,35,36 888888877,888888878,888888880,888888883,888888885,888888886
VBA
<lang vb>Private Function population_count(ByVal number As Long) As Integer
Dim result As Integer
Dim digit As Integer
Do While number > 0
If number Mod 2 = 1 Then
result = result + 1
End If
number = number \ 2
Loop
population_count = result
End Function
Function is_prime(n As Integer) As Boolean
If n < 2 Then
is_prime = False
Exit Function
End If
For i = 2 To Sqr(n)
If n Mod i = 0 Then
is_prime = False
Exit Function
End If
Next i
is_prime = True
End Function
Function pernicious(n As Long)
Dim tmp As Integer tmp = population_count(n) pernicious = is_prime(tmp)
End Function
Public Sub main()
Dim count As Integer
Dim n As Long: n = 1
Do While count < 25
If pernicious(n) Then
Debug.Print n;
count = count + 1
End If
n = n + 1
Loop
Debug.Print
For n = 888888877 To 888888888
If pernicious(n) Then
Debug.Print n;
End If
Next n
End Sub</lang>
- Output:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886
VBScript
<lang vb>'check if the number is pernicious Function IsPernicious(n) IsPernicious = False bin_num = Dec2Bin(n) sum = 0 For h = 1 To Len(bin_num) sum = sum + CInt(Mid(bin_num,h,1)) Next If IsPrime(sum) Then IsPernicious = True End If End Function
'prime number validation Function IsPrime(n) If n = 2 Then IsPrime = True ElseIf n <= 1 Or n Mod 2 = 0 Then IsPrime = False Else IsPrime = True For i = 3 To Int(Sqr(n)) Step 2 If n Mod i = 0 Then IsPrime = False Exit For End If Next End If End Function
'decimal to binary converter Function Dec2Bin(n) q = n Dec2Bin = "" Do Until q = 0 Dec2Bin = CStr(q Mod 2) & Dec2Bin q = Int(q / 2) Loop End Function
'display the first 25 pernicious numbers c = 0 WScript.StdOut.Write "First 25 Pernicious Numbers:" WScript.StdOut.WriteLine For k = 1 To 100 If IsPernicious(k) Then WScript.StdOut.Write k & ", " c = c + 1 End If If c = 25 Then Exit For End If Next WScript.StdOut.WriteBlankLines(2)
'display the pernicious numbers between 888,888,877 to 888,888,888 (inclusive) WScript.StdOut.Write "Pernicious Numbers between 888,888,877 to 888,888,888 (inclusive):" WScript.StdOut.WriteLine For l = 888888877 To 888888888 If IsPernicious(l) Then WScript.StdOut.Write l & ", " End If Next WScript.StdOut.WriteLine</lang>
- Output:
First 25 Pernicious Numbers: 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 31, 33, 34, 35, 36, Pernicious Numbers between 888,888,877 to 888,888,888 (inclusive): 888888877, 888888878, 888888880, 888888883, 888888885, 888888886,
Visual Basic .NET
<lang vbnet>Module Module1
Function PopulationCount(n As Long) As Integer
Dim cnt = 0
Do
If (n Mod 2) <> 0 Then
cnt += 1
End If
n >>= 1
Loop While n > 0
Return cnt
End Function
Function IsPrime(x As Integer) As Boolean
If x <= 2 OrElse (x Mod 2) = 0 Then
Return x = 2
End If
Dim limit = Math.Sqrt(x)
For i = 3 To limit Step 2
If x Mod i = 0 Then
Return False
End If
Next
Return True End Function
Function Pernicious(start As Integer, count As Integer, take As Integer) As IEnumerable(Of Integer)
Return Enumerable.Range(start, count).Where(Function(n) IsPrime(PopulationCount(n))).Take(take)
End Function
Sub Main()
For Each n In Pernicious(0, Integer.MaxValue, 25)
Console.Write("{0} ", n)
Next
Console.WriteLine()
For Each n In Pernicious(888888877, 11, 11)
Console.Write("{0} ", n)
Next
Console.WriteLine()
End Sub
End Module</lang>
- Output:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886
Wortel
The following function returns true if it's argument is a pernicious number: <lang wortel>:ispernum ^(@isPrime \@count \=1 @arr &\`![.toString 2])</lang> Task: <lang wortel>!-ispernum 1..36 ; returns [3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36] !-ispernum 888888877..888888888 ; returns [888888877 888888878 888888880 888888883 888888885 888888886]</lang>
Wren
<lang ecmascript>var pernicious = Fn.new { |w|
var ff = 2.pow(32) - 1 var mask1 = (ff / 3).floor var mask3 = (ff / 5).floor var maskf = (ff / 17).floor var maskp = (ff / 255).floor w = w - (w >> 1 & mask1) w = (w & mask3) + (w >>2 & mask3) w = (w + (w >> 4)) & maskf return 0xa08a28ac >> (w*maskp >> 24) & 1 != 0
}
var i = 0 var n = 1 while (i < 25) {
if (pernicious.call(n)) {
System.write("%(n) ")
i = i + 1
}
n = n + 1
} System.print() for (n in 888888877..888888888) {
if (pernicious.call(n)) System.write("%(n) ")
} System.print()</lang>
- Output:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888888877 888888878 888888880 888888883 888888885 888888886
zkl
The largest number of bits is 30. <lang zkl>primes:=T(2,3,5,7,11,13,17,19,23,29,31,37,41); N:=0; foreach n in ([2..]){
if(n.num1s : primes.holds(_)){
print(n," ");
if((N+=1)==25) break;
}
} foreach n in ([0d888888877..888888888]){
if (n.num1s : primes.holds(_)) "%,d; ".fmt(n).print();
}</lang> Int.num1s returns the number of 1 bits. eg (3).num1s-->2
- Output:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 888,888,877; 888,888,878; 888,888,880; 888,888,883; 888,888,885; 888,888,886;
Or in a more functional style: <lang zkl>primes:=T(2,3,5,7,11,13,17,19,23,29,31,37,41); p:='wrap(n){ primes.holds(n.num1s) };
[1..].filter(25,p).toString(*).println(); [0d888888877..888888888].filter(p).println();</lang> 'wrap is syntactic sugar for a closure - it creates a function that wraps local data (variable primes in this case). We assign that function to p.
- Output:
L(3,5,6,7,9,10,11,12,13,14,17,18,19,20,21,22,24,25,26,28,31,33,34,35,36) L(888888877,888888878,888888880,888888883,888888885,888888886)
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