Factorions
You are encouraged to solve this task according to the task description, using any language you may know.
- Definition
A factorion is a natural number that equals the sum of the factorials of its digits.
- Example
145 is a factorion in base 10 because:
1! + 4! + 5! = 1 + 24 + 120 = 145
It can be shown (see the Wikipedia article below) that no factorion in base 10 can exceed 1,499,999.
- Task
Write a program in your language to demonstrate, by calculating and printing out the factorions, that:
- There are 3 factorions in base 9
- There are 4 factorions in base 10
- There are 5 factorions in base 11
- There are 2 factorions in base 12 (up to the same upper bound as for base 10)
360 Assembly
<lang 360asm>* Factorions 26/04/2020 FACTORIO CSECT
USING FACTORIO,R13 base register
B 72(R15) skip savearea
DC 17F'0' savearea
SAVE (14,12) save previous context
ST R13,4(R15) link backward
ST R15,8(R13) link forward
LR R13,R15 set addressability
XR R4,R4 ~
LA R5,1 f=1
LA R3,FACT+4 @fact(1)
LA R6,1 i=1
DO WHILE=(C,R6,LE,=A(NN2)) do i=1 to nn2
MR R4,R6 fact(i-1)*i
ST R5,0(R3) fact(i)=fact(i-1)*i
LA R3,4(R3) @fact(i+1)
LA R6,1(R6) i++
ENDDO , enddo i
LA R7,NN1 base=nn1
DO WHILE=(C,R7,LE,=A(NN2)) do base=nn1 to nn2
MVC PG,PGX init buffer
LA R3,PG+6 @buffer
XDECO R7,XDEC edit base
MVC PG+5(2),XDEC+10 output base
LA R3,PG+10 @buffer
LA R6,1 i=1
DO WHILE=(C,R6,LE,LIM) do i=1 to lim
LA R9,0 s=0
LR R8,R6 t=i
DO WHILE=(C,R8,NE,=F'0') while t<>0
XR R4,R4 ~
LR R5,R8 t
DR R4,R7 r5=t/base; r4=d=(t mod base)
LR R1,R4 d
SLA R1,2 ~
L R2,FACT(R1) fact(d)
AR R9,R2 s=s+fact(d)
LR R8,R5 t=t/base
ENDDO , endwhile
IF CR,R9,EQ,R6 THEN if s=i then
XDECO R6,XDEC edit i
MVC 0(6,R3),XDEC+6 output i
LA R3,7(R3) @buffer
ENDIF , endif
LA R6,1(R6) i++
ENDDO , enddo i
XPRNT PG,L'PG print buffer
LA R7,1(R7) base++
ENDDO , enddo base
L R13,4(0,R13) restore previous savearea pointer
RETURN (14,12),RC=0 restore registers from calling save
NN1 EQU 9 nn1=9 NN2 EQU 12 nn2=12 LIM DC f'1499999' lim=1499999 FACT DC (NN2+1)F'1' fact(0:12) PG DS CL80 buffer PGX DC CL80'Base .. : ' buffer init XDEC DS CL12 temp fo xdeco
REGEQU
END FACTORIO </lang>
- Output:
Base 9 : 1 2 41282 Base 10 : 1 2 145 40585 Base 11 : 1 2 26 48 40472 Base 12 : 1 2
ALGOL 68
<lang algol68>BEGIN
# cache factorials from 0 to 11 #
[ 0 : 11 ]INT fact;
fact[0] := 1;
FOR n TO 11 DO
fact[n] := fact[n-1] * n
OD;
FOR b FROM 9 TO 12 DO
print( ( "The factorions for base ", whole( b, 0 ), " are:", newline ) );
FOR i TO 1500000 - 1 DO
INT sum := 0;
INT j := i;
WHILE j > 0 DO
sum +:= fact[ j MOD b ];
j OVERAB b
OD;
IF sum = i THEN print( ( whole( i, 0 ), " " ) ) FI
OD;
print( ( newline ) )
OD
END</lang>
- Output:
The factorions for base 9 are: 1 2 41282 The factorions for base 10 are: 1 2 145 40585 The factorions for base 11 are: 1 2 26 48 40472 The factorions for base 12 are: 1 2
Applesoft BASIC
<lang basic>100 DIM FACT(12) 110 FACT(0) = 1 120 FOR N = 1 TO 11 130 FACT(N) = FACT(N - 1) * N 140 NEXT 200 FOR B = 9 TO 12 210 PRINT "THE FACTORIONS "; 215 PRINT "FOR BASE "B" ARE:" 220 FOR I = 1 TO 1499999 230 SUM = 0 240 FOR J = I TO 0 STEP 0 245 M = INT (J / B) 250 D = J - M * B 260 SUM = SUM + FACT(D) 270 J = M 280 NEXT J 290 IF SU = I THEN PRINT I" "; 300 NEXT I 310 PRINT : PRINT 320 NEXT B</lang>
AutoHotkey
<lang AutoHotkey>fact:=[] fact[0] := 1 while (A_Index < 12) fact[A_Index] := fact[A_Index-1] * A_Index b := 9 while (b <= 12) { res .= "base " b " factorions: `t" while (A_Index < 1500000){ sum := 0 j := A_Index while (j > 0){ d := Mod(j, b) sum += fact[d] j /= b } if (sum = A_Index) res .= A_Index " " } b++ res .= "`n" } MsgBox % res return</lang>
- Output:
base 9 factorions: 1 2 41282 base 10 factorions: 1 2 145 40585 base 11 factorions: 1 2 26 48 40472 base 12 factorions: 1 2
AWK
<lang AWK>
- syntax: GAWK -f FACTORIONS.AWK
- converted from C
BEGIN {
fact[0] = 1 # cache factorials from 0 to 11
for (n=1; n<12; ++n) {
fact[n] = fact[n-1] * n
}
for (b=9; b<=12; ++b) {
printf("base %d factorions:",b)
for (i=1; i<1500000; ++i) {
sum = 0
j = i
while (j > 0) {
d = j % b
sum += fact[d]
j = int(j/b)
}
if (sum == i) {
printf(" %d",i)
}
}
printf("\n")
}
exit(0)
} </lang>
- Output:
base 9 factorions: 1 2 41282 base 10 factorions: 1 2 145 40585 base 11 factorions: 1 2 26 48 40472 base 12 factorions: 1 2
C
<lang c>#include <stdio.h>
int main() {
int n, b, d;
unsigned long long i, j, sum, fact[12];
// cache factorials from 0 to 11
fact[0] = 1;
for (n = 1; n < 12; ++n) {
fact[n] = fact[n-1] * n;
}
for (b = 9; b <= 12; ++b) {
printf("The factorions for base %d are:\n", b);
for (i = 1; i < 1500000; ++i) {
sum = 0;
j = i;
while (j > 0) {
d = j % b;
sum += fact[d];
j /= b;
}
if (sum == i) printf("%llu ", i);
}
printf("\n\n");
}
return 0;
}</lang>
- Output:
The factorions for base 9 are: 1 2 41282 The factorions for base 10 are: 1 2 145 40585 The factorions for base 11 are: 1 2 26 48 40472 The factorions for base 12 are: 1 2
C++
<lang cpp>#include <iostream>
class factorion_t { public:
factorion_t() {
f[0] = 1u;
for (uint n = 1u; n < 12u; n++)
f[n] = f[n - 1] * n;
}
bool operator()(uint i, uint b) const {
uint sum = 0;
for (uint j = i; j > 0u; j /= b)
sum += f[j % b];
return sum == i;
}
private:
ulong f[12]; //< cache factorials from 0 to 11
};
int main() {
factorion_t factorion;
for (uint b = 9u; b <= 12u; ++b) {
std::cout << "factorions for base " << b << ':';
for (uint i = 1u; i < 1500000u; ++i)
if (factorion(i, b))
std::cout << ' ' << i;
std::cout << std::endl;
}
return 0;
}</lang>
- Output:
factorions for base 9: 1 2 41282 factorions for base 10: 1 2 145 40585 factorions for base 11: 1 2 26 48 40472 factorions for base 12: 1 2
Delphi
<lang Delphi> program Factorions;
{$APPTYPE CONSOLE}
uses
System.SysUtils;
begin
var fact: TArray<UInt64>; SetLength(fact, 12);
fact[0] := 0; for var n := 1 to 11 do fact[n] := fact[n - 1] * n;
for var b := 9 to 12 do
begin
writeln('The factorions for base ', b, ' are:');
for var i := 1 to 1499999 do
begin
var sum := 0;
var j := i;
while j > 0 do
begin
var d := j mod b;
sum := sum + fact[d];
j := j div b;
end;
if sum = i then
writeln(i, ' ');
end;
writeln(#10);
end;
readln;
end.</lang>
Factor
<lang factor>USING: formatting io kernel math math.parser math.ranges memoize prettyprint sequences ; IN: rosetta-code.factorions
! Memoize factorial function MEMO: factorial ( n -- n! ) [ 1 ] [ [1,b] product ] if-zero ;
- factorion? ( n base -- ? )
dupd >base string>digits [ factorial ] map-sum = ;
- show-factorions ( limit base -- )
dup "The factorions for base %d are:\n" printf [ [1,b) ] dip [ dupd factorion? [ pprint bl ] [ drop ] if ] curry each nl ;
1,500,000 9 12 [a,b] [ show-factorions nl ] with each</lang>
- Output:
The factorions for base 9 are: 1 2 41282 The factorions for base 10 are: 1 2 145 40585 The factorions for base 11 are: 1 2 26 48 40472 The factorions for base 12 are: 1 2
Fōrmulæ
In this page you can see the solution of this task.
Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text (more info). 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 transportation effects more than visualization and edition.
The option to show Fōrmulæ programs and their results is showing images. Unfortunately images cannot be uploaded in Rosetta Code.
FreeBASIC
<lang freebasic>Dim As Integer fact(12), suma, d, j fact(0) = 1 For n As Integer = 1 To 11
fact(n) = fact(n-1) * n
Next n For b As Integer = 9 To 12
Print "Los factoriones para base " & b & " son: "
For i As Integer = 1 To 1499999
suma = 0
j = i
While j > 0
d = j Mod b
suma += fact(d)
j \= b
Wend
If suma = i Then Print i & " ";
Next i
Print : Print
Next b Sleep</lang>
- Output:
Los factoriones para base 9 son: 1 2 41282 Los factoriones para base 10 son: 1 2 145 40585 Los factoriones para base 11 son: 1 2 26 48 40472 Los factoriones para base 12 son: 1 2
Frink
<lang frink>factorion[n, base] := sum[map["factorial", integerDigits[n, base]]]
for base = 9 to 12 {
for n = 1 to 1_499_999
if n == factorion[n, base]
println["$base\t$n"]
}</lang>
- Output:
9 1 9 2 9 41282 10 1 10 2 10 145 10 40585 11 1 11 2 11 26 11 48 11 40472 12 1 12 2
Go
<lang go>package main
import (
"fmt" "strconv"
)
func main() {
// cache factorials from 0 to 11
var fact [12]uint64
fact[0] = 1
for n := uint64(1); n < 12; n++ {
fact[n] = fact[n-1] * n
}
for b := 9; b <= 12; b++ {
fmt.Printf("The factorions for base %d are:\n", b)
for i := uint64(1); i < 1500000; i++ {
digits := strconv.FormatUint(i, b)
sum := uint64(0)
for _, digit := range digits {
if digit < 'a' {
sum += fact[digit-'0']
} else {
sum += fact[digit+10-'a']
}
}
if sum == i {
fmt.Printf("%d ", i)
}
}
fmt.Println("\n")
}
}</lang>
- Output:
The factorions for base 9 are: 1 2 41282 The factorions for base 10 are: 1 2 145 40585 The factorions for base 11 are: 1 2 26 48 40472 The factorions for base 12 are: 1 2
Haskell
<lang haskell>import Text.Printf (printf) import Data.List (unfoldr) import Control.Monad (guard)
factorion :: Int -> Int -> Bool factorion b n = f b n == n
where f b = sum . map (product . enumFromTo 1) . unfoldr (\x -> guard (x > 0) >> pure (x `mod` b, x `div` b))
main :: IO () main = mapM_ (uncurry (printf "Factorions for base %2d: %s\n") . (\(a, b) -> (b, result a b)))
[(3,9), (4,10), (5,11), (2,12)] where factorions b = filter (factorion b) [1..] result n = show . take n . factorions</lang>
- Output:
Factorions for base 9: [1,2,41282] Factorions for base 10: [1,2,145,40585] Factorions for base 11: [1,2,26,48,40472] Factorions for base 12: [1,2]
J
<lang J>
index=: $ #: I.@:, factorion=: 10&$: :(] = [: +/ [: ! #.^:_1)&>
FACTORIONS=: 9 0 +"1 index Q=: 9 10 11 12 factorion/ i. 1500000
NB. base, factorion expressed in bases 10, and base
(,. ".@:((Num_j_,26}.Alpha_j_) {~ #.inv/)"1) FACTORIONS
9 1 1
9 2 2
9 41282 62558
10 1 1 10 2 2 10 145 145 10 40585 40585 11 1 1 11 2 2 11 26 24 11 48 44 11 40472 28453 12 1 1 12 2 2
NB. tallies of factorions in the bases (9+i.4),.+/"1 Q 9 3
10 4 11 5 12 2 </lang>
Java
<lang java> public class Factorion {
public static void main(String [] args){
System.out.println("Base 9:");
for(int i = 1; i <= 1499999; i++){
String iStri = String.valueOf(i);
int multiplied = operate(iStri,9);
if(multiplied == i){
System.out.print(i + "\t");
}
}
System.out.println("\nBase 10:");
for(int i = 1; i <= 1499999; i++){
String iStri = String.valueOf(i);
int multiplied = operate(iStri,10);
if(multiplied == i){
System.out.print(i + "\t");
}
}
System.out.println("\nBase 11:");
for(int i = 1; i <= 1499999; i++){
String iStri = String.valueOf(i);
int multiplied = operate(iStri,11);
if(multiplied == i){
System.out.print(i + "\t");
}
}
System.out.println("\nBase 12:");
for(int i = 1; i <= 1499999; i++){
String iStri = String.valueOf(i);
int multiplied = operate(iStri,12);
if(multiplied == i){
System.out.print(i + "\t");
}
}
}
public static int factorialRec(int n){
int result = 1;
return n == 0 ? result : result * n * factorialRec(n-1);
}
public static int operate(String s, int base){
int sum = 0;
String strx = fromDeci(base, Integer.parseInt(s));
for(int i = 0; i < strx.length(); i++){
if(strx.charAt(i) == 'A'){
sum += factorialRec(10);
}else if(strx.charAt(i) == 'B') {
sum += factorialRec(11);
}else if(strx.charAt(i) == 'C') {
sum += factorialRec(12);
}else {
sum += factorialRec(Integer.parseInt(String.valueOf(strx.charAt(i)), base));
}
}
return sum;
}
// Ln 57-71 from Geeks for Geeks @ https://www.geeksforgeeks.org/convert-base-decimal-vice-versa/
static char reVal(int num) {
if (num >= 0 && num <= 9)
return (char)(num + 48);
else
return (char)(num - 10 + 65);
}
static String fromDeci(int base, int num){
StringBuilder s = new StringBuilder();
while (num > 0) {
s.append(reVal(num % base));
num /= base;
}
return new String(new StringBuilder(s).reverse());
}
} </lang>
- Output:
Base 9: 1 2 41282 Base 10: 1 2 145 40585 Base 11: 1 2 26 48 40472 Base 12: 1 2
Julia
<lang julia>isfactorian(n, base) = mapreduce(factorial, +, map(c -> parse(Int, c, base=16), split(string(n, base=base), ""))) == n
printallfactorian(base) = println("Factorians for base $base: ", [n for n in 1:100000 if isfactorian(n, base)])
foreach(printallfactorian, 9:12)
</lang>
- Output:
Factorians for base 9: [1, 2, 41282] Factorians for base 10: [1, 2, 145, 40585] Factorians for base 11: [1, 2, 26, 48, 40472] Factorians for base 12: [1, 2]
Nim
Note that the library has precomputed the values of factorial, so there is no need for caching. <lang Nim>from math import fac from strutils import join
iterator digits(n, base: Natural): Natural =
## Yield the digits of "n" in base "base". var n = n while true: yield n mod base n = n div base if n == 0: break
func isFactorion(n, base: Natural): bool =
## Return true if "n" is a factorion for base "base". var s = 0 for d in n.digits(base): inc s, fac(d) result = s == n
func factorions(base, limit: Natural): seq[Natural] =
## Return the list of factorions for base "base" up to "limit".
for n in 1..limit:
if n.isFactorion(base):
result.add(n)
for base in 9..12:
echo "Factorions for base ", base, ':'
echo factorions(base, 1_500_000 - 1).join(" ")</lang>
- Output:
Factorions for base 9: 1 2 41282 Factorions for base 10: 1 2 145 40585 Factorions for base 11: 1 2 26 48 40472 Factorions for base 12: 1 2
OCaml
<lang ocaml>let () =
(* cache factorials from 0 to 11 *) let fact = Array.make 12 0 in fact.(0) <- 1; for n = 1 to pred 12 do fact.(n) <- fact.(n-1) * n; done;
for b = 9 to 12 do
Printf.printf "The factorions for base %d are:\n" b;
for i = 1 to pred 1_500_000 do
let sum = ref 0 in
let j = ref i in
while !j > 0 do
let d = !j mod b in
sum := !sum + fact.(d);
j := !j / b;
done;
if !sum = i then (print_int i; print_string " ")
done;
print_string "\n\n";
done</lang>
Perl
<lang perl>use strict; use warnings; use ntheory qw/factorial todigits/;
my $limit = 1500000;
for my $b (9 .. 12) {
print "Factorions in base $b:\n"; $_ == factorial($_) and print "$_ " for 0..$b-1;
for my $i (1 .. int $limit/$b) {
my $sum;
my $prod = $i * $b;
for (reverse todigits($i, $b)) {
$sum += factorial($_);
$sum = 0 && last if $sum > $prod;
}
next if $sum == 0;
($sum + factorial($_) == $prod + $_) and print $prod+$_ . ' ' for 0..$b-1;
}
print "\n\n";
}</lang>
- Output:
Factorions in base 9: 1 2 41282 Factorions in base 10: 1 2 145 40585 Factorions in base 11: 1 2 26 48 40472 Factorions in base 12: 1 2
Alternatively, a more efficient approach:
<lang perl>use 5.020; use ntheory qw(:all); use experimental qw(signatures); use Algorithm::Combinatorics qw(combinations_with_repetition);
sub max_power ($base = 10) {
my $m = 1;
my $f = factorial($base - 1);
while ($m * $f >= $base**($m-1)) {
$m += 1;
}
return $m-1;
}
sub factorions ($base = 10) {
my @result;
my @digits = (0 .. $base-1);
my @factorial = map { factorial($_) } @digits;
foreach my $k (1 .. max_power($base)) {
my $iter = combinations_with_repetition(\@digits, $k);
while (my $comb = $iter->next) {
my $n = vecsum(map { $factorial[$_] } @$comb);
if (join(' ', sort { $a <=> $b } todigits($n, $base)) eq join(' ', @$comb)) {
push @result, $n;
}
}
}
return @result;
}
foreach my $base (2 .. 14) {
my @r = factorions($base); say "Factorions in base $base are (@r)";
}</lang>
- Output:
Factorions in base 2 are (1 2) Factorions in base 3 are (1 2) Factorions in base 4 are (1 2 7) Factorions in base 5 are (1 2 49) Factorions in base 6 are (1 2 25 26) Factorions in base 7 are (1 2) Factorions in base 8 are (1 2) Factorions in base 9 are (1 2 41282) Factorions in base 10 are (1 2 145 40585) Factorions in base 11 are (1 2 26 48 40472) Factorions in base 12 are (1 2) Factorions in base 13 are (1 2 519326767) Factorions in base 14 are (1 2 12973363226)
Phix
<lang Phix>-- cache factorials from 0 to 11 sequence fact = repeat(1,12) for n=2 to length(fact) do
fact[n] = fact[n-1]*(n-1)
end for
for b=9 to 12 do
printf(1,"The factorions for base %d are:\n", b)
for i=1 to 1499999 do
atom total = 0, j = i, d
while j>0 and total<=i do
d = remainder(j,b)
total += fact[d+1]
j = floor(j/b)
end while
if total==i then printf(1,"%d ", i) end if
end for
printf(1,"\n\n")
end for</lang>
- Output:
The factorions for base 9 are: 1 2 41282 The factorions for base 10 are: 1 2 145 40585 The factorions for base 11 are: 1 2 26 48 40472 The factorions for base 12 are: 1 2
Python
<lang Python>fact = [1] # cache factorials from 0 to 11 for n in range(1, 12):
fact.append(fact[n-1] * n)
for b in range(9, 12+1):
print(f"The factorions for base {b} are:")
for i in range(1500000):
fact_sum = 0
j = i
while j > 0:
d = j % b
fact_sum += fact[d]
j = j//b
if fact_sum == i:
print(i, end=" ")
print()
</lang>
- Output:
The factorions for base 9 are: 1 2 41282 The factorions for base 10 are: 1 2 145 40585 The factorions for base 11 are: 1 2 26 48 40472 The factorions for base 12 are: 1 2
Racket
<lang racket>#lang racket
(define fact
(curry list-ref (for/fold ([result (list 1)] #:result (reverse result))
([x (in-range 1 20)])
(cons (* x (first result)) result))))
(for ([b (in-range 9 13)])
(printf "The factorions for base ~a are:\n" b)
(for ([i (in-range 1 1500000)])
(let loop ([sum 0] [n i])
(cond
[(positive? n) (loop (+ sum (fact (modulo n b))) (quotient n b))]
[(= sum i) (printf "~a " i)])))
(newline))</lang>
- Output:
The factorions for base 9 are: 1 2 41282 The factorions for base 10 are: 1 2 145 40585 The factorions for base 11 are: 1 2 26 48 40472 The factorions for base 12 are: 1 2
Raku
(formerly Perl 6)
<lang perl6>constant @factorial = 1, |[\*] 1..*;
constant $limit = 1500000;
constant $bases = 9 .. 12;
my @result;
$bases.race(:1batch).map: -> $base {
@result[$base] = "\nFactorions in base $base:\n1 2";
sink (1 .. $limit div $base).map: -> $i {
my $product = $i * $base;
my $partial;
for $i.polymod($base xx *) {
$partial += @factorial[$_];
last if $partial > $product
}
next if $partial > $product;
my $sum;
for ^$base {
last if ($sum = $partial + @factorial[$_]) > $product + $_;
@result[$base] ~= " $sum" and last if $sum == $product + $_
}
}
}
.say for @result[$bases];</lang>
- Output:
Factorions in base 9: 1 2 41282 Factorions in base 10: 1 2 145 40585 Factorions in base 11: 1 2 26 48 40472 Factorions in base 12: 1 2
REXX
<lang rexx>/*REXX program calculates and displays factorions in bases nine ───► twelve. */ parse arg LOb HIb lim . /*obtain optional arguments from the CL*/ if LOb== | LOb=="," then LOb= 9 /*Not specified? Then use the default.*/ if HIb== | HIb=="," then HIb= 12 /* " " " " " " */ if lim== | lim=="," then lim= 1500000 - 1 /* " " " " " " */
do fact=0 to HIb; !.fact= !(fact) /*use memoization for factorials. */ end /*fact*/
do base=LOb to HIb /*process all the required bases. */
@= 1 2 /*initialize the list (@) to 1 & 2. */
do j=3 for lim-2; $= 0 /*initialize the sum ($) to zero. */
t= j /*define the target (for the sum !'s).*/
do until t==0; d= t // base /*obtain a "digit".*/
$= $ + !.d /*add !(d) to sum.*/
t= t % base /*get a new target.*/
end /*until*/
if $==j then @= @ j /*Good factorial sum? Then add to list.*/
end /*i*/
say
say 'The factorions for base ' right( base, length(HIb) ) " are: " @
end /*base*/
exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ !: procedure; parse arg x; !=1; do j=2 to x; !=!*j; end; return ! /*factorials*/</lang>
- output when using the default inputs:
The factorions for base 9 are: 1 2 41282 The factorions for base 10 are: 1 2 145 40585 The factorions for base 11 are: 1 2 26 48 40472 The factorions for base 12 are: 1 2
Ring
<lang Ring> load "stdlib.ring"
for n = 1 to 100000
fac = 0
numStr = string(n)
for m = 1 to len(numStr)
num = number(numStr[m])
fac = fac + factorial(num)
next
if n = fac
see "Factorion: " + n + nl
ok
next </lang>
Factorion: 1 Factorion: 2 Factorion: 145 Factorion: 40585
Ruby
<lang ruby> def factorion?(n, base)
n.digits(base).sum{|digit| (1..digit).inject(1, :*)} == n
end
(9..12).each do |base|
puts "Base #{base} factorions: #{(1..1_500_000).select{|n| factorion?(n, base)}.join(" ")} "
end </lang>
- Output:
Base 9 factorions: 1 2 41282 Base 10 factorions: 1 2 145 40585 Base 11 factorions: 1 2 26 48 40472 Base 12 factorions: 1 2
Scala
<lang scala>object Factorion extends App {
private def is_factorion(i: Int, b: Int): Boolean = {
var sum = 0L
var j = i
while (j > 0) {
sum += f(j % b)
j /= b
}
sum == i
}
private val f = Array.ofDim[Long](12)
f(0) = 1L
(1 until 12).foreach(n => f(n) = f(n - 1) * n)
(9 to 12).foreach(b => {
print(s"factorions for base $b:")
(1 to 1500000).filter(is_factorion(_, b)).foreach(i => print(s" $i"))
println
})
}</lang>
Sidef
<lang ruby>func max_power(b = 10) {
var m = 1
var f = (b-1)!
while (m*f >= b**(m-1)) {
m += 1
}
return m-1
}
func factorions(b = 10) {
var result = []
var digits = @^b
var fact = digits.map { _! }
for k in (1 .. max_power(b)) {
digits.combinations_with_repetition(k, {|*comb|
var n = comb.sum_by { fact[_] }
if (n.digits(b).sort == comb) {
result << n
}
})
}
return result
}
for b in (2..12) {
var r = factorions(b)
say "Base #{'%2d' % b} factorions: #{r}"
}</lang>
- Output:
Base 2 factorions: [1, 2] Base 3 factorions: [1, 2] Base 4 factorions: [1, 2, 7] Base 5 factorions: [1, 2, 49] Base 6 factorions: [1, 2, 25, 26] Base 7 factorions: [1, 2] Base 8 factorions: [1, 2] Base 9 factorions: [1, 2, 41282] Base 10 factorions: [1, 2, 145, 40585] Base 11 factorions: [1, 2, 26, 48, 40472] Base 12 factorions: [1, 2]
Swift
<lang swift>var fact = Array(repeating: 0, count: 12)
fact[0] = 1
for n in 1..<12 {
fact[n] = fact[n - 1] * n
}
for b in 9...12 {
print("The factorions for base \(b) are:")
for i in 1..<1500000 {
var sum = 0
var j = i
while j > 0 {
sum += fact[j % b]
j /= b
}
if sum == i {
print("\(i)", terminator: " ")
fflush(stdout)
}
}
print("\n")
}</lang>
- Output:
The factorions for base 9 are: 1 2 41282 The factorions for base 10 are: 1 2 145 40585 The factorions for base 11 are: 1 2 26 48 40472 The factorions for base 12 are: 1 2
Wren
<lang ecmascript>// cache factorials from 0 to 11 var fact = List.filled(12, 0) fact[0] = 1 for (n in 1..11) fact[n] = fact[n-1] * n
for (b in 9..12) {
System.print("The factorions for base %(b) are:")
for (i in 1...1500000) {
var sum = 0
var j = i
while (j > 0) {
var d = j % b
sum = sum + fact[d]
j = (j/b).floor
}
if (sum == i) System.write("%(i) ")
}
System.print("\n")
}</lang>
- Output:
The factorions for base 9 are: 1 2 41282 The factorions for base 10 are: 1 2 145 40585 The factorions for base 11 are: 1 2 26 48 40472 The factorions for base 12 are: 1 2
VBScript
<lang vb>' Factorions - VBScript - PG - 26/04/2020
Dim fact()
nn1=9 : nn2=12 lim=1499999
ReDim fact(nn2)
fact(0)=1 For i=1 To nn2 fact(i)=fact(i-1)*i Next For base=nn1 To nn2 list="" For i=1 To lim s=0 t=i Do While t<>0 d=t Mod base s=s+fact(d) t=t\base Loop If s=i Then list=list &" "& i Next Wscript.Echo "the factorions for base "& right(" "& base,2) &" are: "& list Next </lang>
- Output:
the factorions for base 9 are: 1 2 41282 the factorions for base 10 are: 1 2 145 40585 the factorions for base 11 are: 1 2 26 48 40472 the factorions for base 12 are: 1 2
zkl
<lang zkl>var facts=[0..12].pump(List,fcn(n){ (1).reduce(n,fcn(N,n){ N*n },1) }); #(1,1,2,6....) fcn factorions(base){
fs:=List();
foreach n in ([1..1_499_999]){
sum,j := 0,n;
while(j){
sum+=facts[j%base]; j/=base;
}
if(sum==n) fs.append(n);
}
fs
}</lang> <lang zkl>foreach n in ([9..12]){
println("The factorions for base %2d are: ".fmt(n),factorions(n).concat(" "));
}</lang>
- Output:
The factorions for base 9 are: 1 2 41282 The factorions for base 10 are: 1 2 145 40585 The factorions for base 11 are: 1 2 26 48 40472 The factorions for base 12 are: 1 2