Cullen and Woodall numbers: Difference between revisions
Add Scala implementation
(Added Sidef) |
(Add Scala implementation) |
||
| (46 intermediate revisions by 23 users not shown) | |||
Line 1:
{{
A [[wp:Cullen_number|Cullen number]] is a number of the form <span style="font-size:125%;">'''n × 2<sup>n</sup> + 1'''</span> where <span style="font-size:125%;">'''n'''</span> is a natural number.
Line 39:
* [[oeis:A002234|OEIS:A002234 - Numbers k such that the Woodall number k*2^k - 1 is prime]]
=={{header|11l}}==
{{trans|Python}}
<syntaxhighlight lang="11l">
F cullen(n)
R (n << n) + 1
F woodall(n)
R (n << n) - 1
print(‘First 20 Cullen numbers:’)
L(i) 1..20
print(cullen(i), end' ‘ ’)
print()
print()
print(‘First 20 Woodall numbers:’)
L(i) 1..20
print(woodall(i), end' ‘ ’)
print()
</syntaxhighlight>
{{out}}
<pre>
First 20 Cullen numbers:
3 9 25 65 161 385 897 2049 4609 10241 22529 49153 106497 229377 491521 1048577 2228225 4718593 9961473 20971521
First 20 Woodall numbers:
1 7 23 63 159 383 895 2047 4607 10239 22527 49151 106495 229375 491519 1048575 2228223 4718591 9961471 20971519
</pre>
=={{header|ALGOL 68}}==
Line 44 ⟶ 74:
Uses Algol 68Gs LONG LONG INT for long integers. The number of digits must be specified and appears to affect the run time as larger sies are specified. This sample only shows the first two Cullen primes as the time taken to find the third is rather long.
{{libheader|ALGOL 68-primes}}
<
# a Cullen number n is n2^2 + 1, Woodall number is n2^n - 1 #
PR read "primes.incl.a68" PR # include prime utilities #
Line 93 ⟶ 123:
print( ( newline ) )
END
END</
{{out}}
<pre>
Line 101 ⟶ 131:
Index of the 1st 12 Woodall primes: 2 3 6 30 75 81 115 123 249 362 384 462
</pre>
=={{header|Arturo}}==
<syntaxhighlight lang="rebol">cullen: function [n]->
inc n * 2^n
woodall: function [n]->
dec n * 2^n
print ["First 20 cullen numbers:" join.with:" " to [:string] map 1..20 => cullen]
print ["First 20 woodall numbers:" join.with:" " to [:string] map 1..20 => woodall]</syntaxhighlight>
{{out}}
<pre>First 20 cullen numbers: 3 9 25 65 161 385 897 2049 4609 10241 22529 49153 106497 229377 491521 1048577 2228225 4718593 9961473 20971521
First 20 woodall numbers: 1 7 23 63 159 383 895 2047 4607 10239 22527 49151 106495 229375 491519 1048575 2228223 4718591 9961471 20971519</pre>
=={{header|Asymptote}}==
<syntaxhighlight lang="Asymptote">int num = 0;
write("First 20 Cullen numbers:");
for(int n = 1; n < 20; ++n) {
num = n * (2^n) + 1;
write(" ", num, suffix=none);
}
write("");
write("First 20 Woodall numbers:");
for(int n = 1; n < 20; ++n) {
num = n * (2^n) - 1;
write(" ", num, suffix=none);
}</syntaxhighlight>
=={{header|AWK}}==
<syntaxhighlight lang="awk">
# syntax: GAWK -f CULLEN_AND_WOODALL_NUMBERS.AWK
BEGIN {
Line 119 ⟶ 184:
exit(0)
}
</syntaxhighlight>
{{out}}
<pre>
Line 127 ⟶ 192:
=={{header|BASIC}}==
==={{header|Applesoft BASIC}}===
{{works with|Chipmunk Basic}}
{{trans|Chipmunk Basic}}
<syntaxhighlight lang="qbasic">10 REM Cullen and Woodall numbers
20 HOME : REM 20 CLS for Chipmunk Basic
30 PRINT "First 20 Cullen numbers:"
40 FOR n = 1 TO 20
50 num = n*(2^n)+1
60 PRINT INT(num);" ";
70 NEXT
80 PRINT : PRINT
90 PRINT "First 20 Woodall numbers:"
100 FOR n = 1 TO 20
110 num = n*(2^n)-1
120 PRINT INT(num);" ";
130 NEXT n
140 END</syntaxhighlight>
==={{header|BASIC256}}===
{{works with|Run BASIC}}
{{works with|Just BASIC}}
{{works with|Liberty BASIC}}
{{trans|FreeBASIC}}
<
for n = 1 to 20
Line 143 ⟶ 229:
print int(num); " ";
next n
end</
{{out}}
<pre>Igual que la entrada de FreeBASIC.</pre>
==={{header|Chipmunk Basic}}===
{{works with|Chipmunk Basic|3.6.4}}
{{works with|Applesoft BASIC}}
{{works with|MSX_BASIC}}
{{works with|PC-BASIC|any}}
{{works with|QBasic}}
{{trans|FreeBASIC}}
<syntaxhighlight lang="qbasic">10 REM Cullen and Woodall numbers
20 CLS : REM 20 HOME for Applesoft BASIC
30 PRINT "First 20 Cullen numbers:"
40 FOR n = 1 TO 20
50 num = n*(2^n)+1
60 PRINT INT(num);" ";
70 NEXT
80 PRINT : PRINT
90 PRINT "First 20 Woodall numbers:"
100 FOR n = 1 TO 20
110 num = n*(2^n)-1
120 PRINT INT(num);" ";
130 NEXT n
140 END</syntaxhighlight>
{{out}}
<pre>Same as FreeBASIC entry.</pre>
==={{header|FreeBASIC}}===
<
Print "First 20 Cullen numbers:"
Line 164 ⟶ 272:
Print num; " ";
Next n
Sleep</
{{out}}
<pre>First 20 Cullen numbers:
Line 171 ⟶ 279:
First 20 Woodall numbers:
1 7 23 63 159 383 895 2047 4607 10239 22527 49151 106495 229375 491519 1048575 2228223 4718591 9961471 20971519</pre>
==={{header|Gambas}}===
<syntaxhighlight lang="vbnet">Public Sub Main()
Dim n, num As Integer
Print "First 20 Cullen numbers:"
For n = 1 To 20
num = n * (2 ^ n) + 1
Print num; " ";
Next
Print "\n\nFirst 20 Woodall numbers:"
For n = 1 To 20
num = n * (2 ^ n) - 1
Print num; " ";
Next
End </syntaxhighlight>
{{out}}
<pre>Same as FreeBASIC entry.</pre>
==={{header|GW-BASIC}}===
The [[#Chipmunk_Basic|Chipmunk Basic]] solution works without any changes.
==={{header|PureBasic}}===
<
PrintN("First 20 Cullen numbers:")
Line 189 ⟶ 323:
PrintN(#CRLF$ + "--- terminado, pulsa RETURN---"): Input()
CloseConsole()</
{{out}}
<pre>Igual que la entrada de FreeBASIC.</pre>
==={{header|QBasic}}===
Line 200 ⟶ 332:
{{works with|True BASIC}}
{{trans|FreeBASIC}}
<
PRINT "First 20 Cullen numbers:"
Line 216 ⟶ 348:
PRINT num;
NEXT n
END</
{{out}}
<pre>Igual que la entrada de FreeBASIC.</pre>
==={{header|Run BASIC}}===
{{works with|BASIC256}}
{{works with|Just BASIC}}
{{works with|Liberty BASIC}}
<syntaxhighlight lang="vb">print "First 20 Cullen numbers:"
for n = 1 to 20
num = n * (2^n)+1
print int(num); " ";
next
print : print
print "First 20 Woodall numbers:"
for n = 1 to 20
num = n * (2^n)-1
print int(num); " ";
next n
end</syntaxhighlight>
{{out}}
<pre>Same as FreeBASIC entry.</pre>
==={{Header|Tiny BASIC}}===
<syntaxhighlight lang="qbasic">REM Rosetta Code problem: https://rosettacode.org/wiki/Cullen_and_Woodall_numbers
REM by Jjuanhdez, 03/2023
REM TinyBasic does not support values greater than 32767
PRINT "First 11 Cullen numbers:"
LET N = 0
LET I = 1
10 IF I = 12 THEN GOTO 20
GOSUB 50
LET N = (I*R) +1
PRINT N, " "
LET I = I+1
GOTO 10
20 PRINT ""
PRINT "First 11 Woodall numbers:"
LET I = 1
30 IF I = 12 THEN GOTO 40
GOSUB 50
LET N = (I*R) -1
PRINT N, " "
LET I = I+1
GOTO 30
40 END
50 REM Exponent calculation
LET A = 2
LET B = I
LET X = 1
LET R = 2
60 IF X >= B THEN RETURN
LET T = R
IF R < A THEN LET R = A*A
IF T < A THEN GOTO 70
IF R >= A THEN LET R = R*A
70 LET X = X+1
GOTO 60</syntaxhighlight>
{{out}}
<pre>First 11 Cullen numbers:
3
9
25
65
161
385
897
2049
4609
10241
22529
First 11 Woodall numbers:
1
7
23
63
159
383
895
2047
4607
10239
22527</pre>
==={{header|True BASIC}}===
{{works with|QBasic}}
{{trans|FreeBASIC}}
<
PRINT "First 20 Cullen numbers:"
Line 241 ⟶ 458:
PRINT num;
NEXT n
END</
{{out}}
<pre>Igual que la entrada de FreeBASIC.</pre>
==={{header|MSX Basic}}===
The [[#Chipmunk_Basic|Chipmunk Basic]] solution works without any changes.
==={{header|XBasic}}===
{{works with|Windows XBasic}}
<syntaxhighlight lang="qbasic">PROGRAM "progname"
VERSION "0.0000"
IMPORT "xma"
DECLARE FUNCTION Entry ()
FUNCTION Entry ()
PRINT "First 20 Cullen numbers:"
FOR n = 1 TO 20
num! = n * POWER (2, n) + 1
PRINT num!;
NEXT n
PRINT
PRINT
PRINT "First 20 Woodall numbers:"
FOR n = 1 TO 20
num! = n * POWER (2, n) - 1
PRINT num!;
NEXT n
END FUNCTION
END PROGRAM</syntaxhighlight>
==={{header|Yabasic}}===
<
for n = 1 to 20
Line 262 ⟶ 510:
next n
print
end</
{{out}}
<pre>Igual que la entrada de FreeBASIC.</pre>
=={{header|C++}}==
<syntaxhighlight lang="c++">
#include <cstdint>
#include <iostream>
#include <string>
uint32_t number, power;
void number_initialise() {
number = 0;
power = 1;
}
enum NumberType { Cullen, Woodhall };
uint32_t next_number(const NumberType& number_type) {
number += 1;
power <<= 1;
switch ( number_type ) {
case Cullen: return number * power + 1;
case Woodhall: return number * power - 1;
};
return 0;
}
void number_sequence(const uint32_t& count, const NumberType& number_type) {
std::string type = ( number_type == Cullen ) ? "Cullen" : "Woodhall";
std::cout << "The first " << count << " " << type << " numbers are:" << std::endl;
number_initialise();
for ( uint32_t index = 1; index <= count; ++index ) {
std::cout << next_number(number_type) << " ";
}
std::cout << std::endl << std::endl;
}
int main() {
number_sequence(20, Cullen);
number_sequence(20, Woodhall);
}
</syntaxhighlight>
{{ out }}
<pre>
The first 20 Cullen numbers are:
3 9 25 65 161 385 897 2049 4609 10241 22529 49153 106497 229377 491521 1048577 2228225 4718593 9961473 20971521
The first 20 Woodhall numbers are:
1 7 23 63 159 383 895 2047 4607 10239 22527 49151 106495 229375 491519 1048575 2228223 4718591 9961471 20971519
</pre>
=={{header|Delphi}}==
{{works with|Delphi|6.0}}
{{libheader|SysUtils,StdCtrls}}
<syntaxhighlight lang="Delphi">
uses SysUtils,StdCtrls;
procedure CullenWoodallTest(Memo: TMemo);
implementation
procedure FindCullenNumbers(Memo: TMemo);
var N,R: integer;
var S: string;
begin
S:='';
Memo.Lines.Add('First 20 Cullen Numbers:');
for N:=1 to 20 do
begin
R:=N * (1 shl N) + 1;
S:=S+IntToStr(R)+' ';
end;
Memo.Lines.Add(S);
end;
procedure FindWoodallNumbers(Memo: TMemo);
var N,R: integer;
var S: string;
begin
S:='';
Memo.Lines.Add('First 20 Woodall Numbers:');
for N:=1 to 20 do
begin
R:=N * (1 shl N) - 1;
S:=S+IntToStr(R)+' ';
end;
Memo.Lines.Add(S);
end;
procedure CullenWoodallTest(Memo: TMemo);
begin
FindCullenNumbers(Memo);
FindWoodallNumbers(Memo);
end;
</syntaxhighlight>
{{out}}
<pre>
First 20 Cullen Numbers:
3 9 25 65 161 385 897 2049 4609 10241 22529 49153 106497 229377 491521 1048577 2228225 4718593 9961473 20971521
First 20 Woodall Numbers:
1 7 23 63 159 383 895 2047 4607 10239 22527 49151 106495 229375 491519 1048575 2228223 4718591 9961471 20971519
</pre>
=={{header|EasyLang}}==
<syntaxhighlight lang="easylang">
for n = 1 to 20
write n * pow 2 n + 1 & " "
.
print ""
for n = 1 to 20
write n * pow 2 n - 1 & " "
.
print ""
</syntaxhighlight>
=={{header|F_Sharp|F#}}==
<
// Cullen and Woodall numbers. Nigel Galloway: January 14th., 2022
let Cullen,Woodall=let fG n (g:int)=(bigint g)*2I**g+n in fG 1I, fG -1I
Line 277 ⟶ 640:
Seq.initInfinite((+)1)|>Seq.filter(fun n->let mutable n=Woodall n in Open.Numeric.Primes.MillerRabin.IsProbablePrime &n)|>Seq.take 12|>Seq.iter(printf "%A "); printfn ""
Seq.initInfinite((+)1)|>Seq.filter(fun n->let mutable n=Cullen n in Open.Numeric.Primes.MillerRabin.IsProbablePrime &n)|>Seq.take 5|>Seq.iter(printf "%A "); printfn ""
</syntaxhighlight>
{{out}}
<pre>
Line 285 ⟶ 648:
1 141 4713 5795 6611
</pre>
=={{header|Factor}}==
{{works with|Factor|0.99 2022-04-03}}
<syntaxhighlight lang="factor">USING: arrays kernel math math.vectors prettyprint ranges
sequences ;
20 [1..b] [ dup 2^ * 1 + ] map dup 2 v-n 2array simple-table.</syntaxhighlight>
{{out}}
<pre>
3 9 25 65 161 385 897 2049 4609 10241 22529 49153 106497 229377 491521 1048577 2228225 4718593 9961473 20971521
1 7 23 63 159 383 895 2047 4607 10239 22527 49151 106495 229375 491519 1048575 2228223 4718591 9961471 20971519
</pre>
=={{header|FutureBasic}}==
<syntaxhighlight lang="futurebasic">
local fn CullenAndWoodall( limit as long )
NSUInteger i, cullen, woodall
printf @"%13s %9s", fn StringUTF8String( @"Cullen" ), fn StringUTF8String( @"Woodall" )
for i = 1 to limit
cullen = i * ( 2^i ) + 1
woodall = i * ( 2^i ) - 1
printf @"%3lu %9lu %9lu", i, cullen, woodall
next
end fn
fn CullenAndWoodall( 20 )
HandleEvents
</syntaxhighlight>
{{output}}
<pre>
Cullen Woodall
1 3 1
2 9 7
3 25 23
4 65 63
5 161 159
6 385 383
7 897 895
8 2049 2047
9 4609 4607
10 10241 10239
11 22529 22527
12 49153 49151
13 106497 106495
14 229377 229375
15 491521 491519
16 1048577 1048575
17 2228225 2228223
18 4718593 4718591
19 9961473 9961471
20 20971521 20971519
</pre>
=={{header|Go}}==
{{libheader|GMP(Go wrapper)}}
<
import (
Line 339 ⟶ 757:
}
fmt.Println()
}</
{{out}}
Line 355 ⟶ 773:
2 3 6 30 75 81 115 123 249 362 384 462
</pre>
=={{header|Haskell}}==
<syntaxhighlight lang="haskell">findCullen :: Int -> Integer
findCullen n = toInteger ( n * 2 ^ n + 1 )
cullens :: [Integer]
cullens = map findCullen [1 .. 20]
woodalls :: [Integer]
woodalls = map (\i -> i - 2 ) cullens
main :: IO ( )
main = do
putStrLn "First 20 Cullen numbers:"
print cullens
putStrLn "First 20 Woodall numbers:"
print woodalls</syntaxhighlight>
{{out}}
<pre>First 20 Cullen numbers:
[3,9,25,65,161,385,897,2049,4609,10241,22529,49153,106497,229377,491521,1048577,2228225,4718593,9961473,20971521]
First 20 Woodall numbers:
[1,7,23,63,159,383,895,2047,4607,10239,22527,49151,106495,229375,491519,1048575,2228223,4718591,9961471,20971519]
</pre>
=={{header|J}}==
<syntaxhighlight lang="j">cullen=: {{ y* 1+2x^y }}
woodall=: {{ y*_1+2x^y }}</syntaxhighlight>
Task example:
<syntaxhighlight lang="j"> cullen 1+i.20
3 10 27 68 165 390 903 2056 4617 10250 22539 49164 106509 229390 491535 1048592 2228241 4718610 9961491 20971540
woodall 1+i.20
1 6 21 60 155 378 889 2040 4599 10230 22517 49140 106483 229362 491505 1048560 2228207 4718574 9961453 20971500</syntaxhighlight>
=={{header|Java}}==
<syntaxhighlight lang="java">
import java.math.BigInteger;
public final class CullenAndWoodhall {
public static void main(String[] aArgs) {
numberSequence(20, NumberType.Cullen);
numberSequence(20, NumberType.Woodhall);
primeSequence(5, NumberType.Cullen);
primeSequence(12, NumberType.Woodhall);
}
private enum NumberType { Cullen, Woodhall }
private static void numberSequence(int aCount, NumberType aNumberType) {
System.out.println();
System.out.println("The first " + aCount + " " + aNumberType + " numbers are:");
numberInitialise();
for ( int index = 1; index <= aCount; index++ ) {
System.out.print(nextNumber(aNumberType) + " ");
}
System.out.println();
}
private static void primeSequence(int aCount, NumberType aNumberType) {
System.out.println();
System.out.println("The indexes of the first " + aCount + " " + aNumberType + " primes are:");
primeInitialise();
while ( count < aCount ) {
if ( nextNumber(aNumberType).isProbablePrime(CERTAINTY) ) {
System.out.print(primeIndex + " ");
count += 1;
}
primeIndex += 1;
}
System.out.println();
}
private static BigInteger nextNumber(NumberType aNumberType) {
number = number.add(BigInteger.ONE);
power = power.shiftLeft(1);
return switch ( aNumberType ) {
case Cullen -> number.multiply(power).add(BigInteger.ONE);
case Woodhall -> number.multiply(power).subtract(BigInteger.ONE);
};
}
private static void numberInitialise() {
number = BigInteger.ZERO;
power = BigInteger.ONE;
}
private static void primeInitialise() {
count = 0;
primeIndex = 1;
numberInitialise();
}
private static BigInteger number;
private static BigInteger power;
private static int count;
private static int primeIndex;
private static final int CERTAINTY = 20;
}
</syntaxhighlight>
{{ out }}
<pre>
The first 20 Cullen numbers are:
3 9 25 65 161 385 897 2049 4609 10241 22529 49153 106497 229377 491521 1048577 2228225 4718593 9961473 20971521
The first 20 Woodhall numbers are:
1 7 23 63 159 383 895 2047 4607 10239 22527 49151 106495 229375 491519 1048575 2228223 4718591 9961471 20971519
The indexes of the first 5 Cullen primes are:
1 141 4713 5794 6611
The indexes of the first 12 Woodhall primes are:
2 3 6 30 75 81 115 123 249 362 384 462
</pre>
=={{header|jq}}==
'''Works with jq and gojq, the C and Go implementations of jq'''
The algorithm for checking whether a number is prime is too slow for finding more than the first Cullen prime,
or more than the first four Woodall primes.
<syntaxhighlight lang=jq>
def is_prime:
. as $n
| if ($n < 2) then false
elif ($n % 2 == 0) then $n == 2
elif ($n % 3 == 0) then $n == 3
elif ($n % 5 == 0) then $n == 5
elif ($n % 7 == 0) then $n == 7
elif ($n % 11 == 0) then $n == 11
elif ($n % 13 == 0) then $n == 13
elif ($n % 17 == 0) then $n == 17
elif ($n % 19 == 0) then $n == 19
else
($n | sqrt) as $rt
| 23
| until( . > $rt or ($n % . == 0); .+2)
| . > $rt
end;
def ipow($m; $n): reduce range(0;$n) as $i (1; $m * .);
def cullen: ipow(2;.) * . + 1;
def woodall: cullen - 2;
def task:
"First 20 Cullen numbers (n * 2^n + 1):",
(range(1; 21) | cullen),
"\n\nFirst 20 Woodall numbers (n * 2^n - 1):",
(range(1; 21) | woodall),
"\n\nFirst Cullen primes (in terms of n):",
limit(1;
range(1; infinite)
| select(cullen|is_prime) ),
"\n\nFirst 4 Woodall primes (in terms of n):",
limit(4;
range(0; infinite)
| select(woodall|is_prime) ) ;
task
</syntaxhighlight>
{{output}}
<pre>
First 20 Cullen numbers (n * 2^n + 1):
3
9
25
65
161
385
897
2049
4609
10241
22529
49153
106497
229377
491521
1048577
2228225
4718593
9961473
20971521
First 20 Woodall numbers (n * 2^n - 1):
1
7
23
63
159
383
895
2047
4607
10239
22527
49151
106495
229375
491519
1048575
2228223
4718591
9961471
20971519
First Cullen primes (in terms of n):
1
First 4 Woodall primes (in terms of n):
2
3
6
30
</pre>
=={{header|Julia}}==
{{trans|Raku}}
<
using Primes
Line 370 ⟶ 1,020:
println("\nFirst 5 Cullen primes: (in terms of n)\n", take(5, primecullens)) # A005849
println("\nFirst 12 Woodall primes: (in terms of n)\n", Int.(collect(take(12, primewoodalls)))) # A002234
</
<pre>
First 20 Cullen numbers: ( n × 2**n + 1)
Line 382 ⟶ 1,032:
First 12 Woodall primes: (in terms of n)
[2, 3, 6, 30, 75, 81, 115, 123, 249, 362, 384, 462]
</pre>
=={{header|Lua}}==
<syntaxhighlight lang="lua">function T(t) return setmetatable(t, {__index=table}) end
table.range = function(t,n) local s=T{} for i=1,n do s[i]=i end return s end
table.map = function(t,f) local s=T{} for i=1,#t do s[i]=f(t[i]) end return s end
function cullen(n) return (n<<n)+1 end
print("First 20 Cullen numbers:")
print(T{}:range(20):map(cullen):concat(" "))
function woodall(n) return (n<<n)-1 end
print("First 20 Woodall numbers:")
print(T{}:range(20):map(woodall):concat(" "))</syntaxhighlight>
{{out}}
<pre>First 20 Cullen numbers:
3 9 25 65 161 385 897 2049 4609 10241 22529 49153 106497 229377 491521 1048577 2228225 4718593 9961473 20971521
First 20 Woodall numbers:
1 7 23 63 159 383 895 2047 4607 10239 22527 49151 106495 229375 491519 1048575 2228223 4718591 9961471 20971519</pre>
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">ClearAll[CullenNumber, WoodallNumber]
SetAttributes[{CullenNumber, WoodallNumber}, Listable]
CullenNumber[n_Integer] := n 2^n + 1
WoodallNumber[n_Integer] := n 2^n - 1
CullenNumber[Range[20]]
WoodallNumber[Range[20]]
cps = {};
Do[
If[PrimeQ[CullenNumber[i]],
AppendTo[cps, i];
If[Length[cps] >= 5, Break[]]
]
,
{i, 1, \[Infinity]}
]
cps
wps = {};
Do[
If[PrimeQ[WoodallNumber[i]],
AppendTo[wps, i];
If[Length[wps] >= 12, Break[]]
]
,
{i, 1, \[Infinity]}
];
wps</syntaxhighlight>
{{out}}
<pre>{3, 9, 25, 65, 161, 385, 897, 2049, 4609, 10241, 22529, 49153, 106497, 229377, 491521, 1048577, 2228225, 4718593, 9961473, 20971521}
{1, 7, 23, 63, 159, 383, 895, 2047, 4607, 10239, 22527, 49151, 106495, 229375, 491519, 1048575, 2228223, 4718591, 9961471, 20971519}
{1, 141, 4713, 5795, 6611}
{2, 3, 6, 30, 75, 81, 115, 123, 249, 362, 384, 462}</pre>
=={{header|Maxima}}==
<syntaxhighlight lang="maxima">
/* Functions */
cullen(n):=(n*2^n)+1$
woodall(n):=(n*2^n)-1$
/* Test cases */
makelist(cullen(i),i,20);
makelist(woodall(i),i,20);
</syntaxhighlight>
{{out}}
<pre>
[3,9,25,65,161,385,897,2049,4609,10241,22529,49153,106497,229377,491521,1048577,2228225,4718593,9961473,20971521]
[1,7,23,63,159,383,895,2047,4607,10239,22527,49151,106495,229375,491519,1048575,2228223,4718591,9961471,20971519]
</pre>
=={{header|Nim}}==
{{libheader|Integers}}
<syntaxhighlight lang="Nim">import std/strformat
import integers
iterator cullenNumbers(): (int, Integer) =
var n = 1
var p = newInteger(2)
while true:
yield (n , n * p + 1)
inc n
p = p shl 1
iterator woodallNumbers(): (int, Integer) =
var n = 1
var p = newInteger(2)
while true:
yield (n , n * p - 1)
inc n
p = p shl 1
echo "First 20 Cullen numbers:"
for (n, cn) in cullenNumbers():
stdout.write &"{cn:>9}"
if n mod 5 == 0: echo()
if n == 20: break
echo "\nFirst 20 Woodall numbers:"
for (n, wn) in woodallNumbers():
stdout.write &"{wn:>9}"
if n mod 5 == 0: echo()
if n == 20: break
echo "\nFirst 5 Cullen primes (in terms of n):"
var count = 0
for (n, cn) in cullenNumbers():
if cn.isPrime:
stdout.write ' ', n
inc count
if count == 5: break
echo()
echo "\nFirst 12 Woodall primes (in terms of n):"
count = 0
for (n, wn) in woodallNumbers():
if wn.isPrime:
stdout.write ' ', n
inc count
if count == 12: break
echo()
</syntaxhighlight>
{{out}}
<pre>First 20 Cullen numbers:
3 9 25 65 161
385 897 2049 4609 10241
22529 49153 106497 229377 491521
1048577 2228225 4718593 9961473 20971521
First 20 Woodall numbers:
1 7 23 63 159
383 895 2047 4607 10239
22527 49151 106495 229375 491519
1048575 2228223 4718591 9961471 20971519
First 5 Cullen primes (in terms of n):
1 141 4713 5795 6611
First 12 Woodall primes (in terms of n):
2 3 6 30 75 81 115 123 249 362 384 462
</pre>
=={{header|PARI/GP}}==
<syntaxhighlight lang="PARI/GP">
/* Define the Cullen and Woodall number functions */
cullen(n) = n * 2^n + 1;
woodall(n) = n * 2^n - 1;
{
/* Generate the first 20 Cullen and Woodall numbers */
print(vector(20, n, cullen(n)));
print(vector(20, n, woodall(n)));
/* Find the first 5 Cullen prime numbers */
cps = [];
for(i = 1, +oo,
if(isprime(cullen(i)),
cps = concat(cps, i);
if(#cps >= 5, break);
);
);
print(cps);
/* Find the first 12 Woodall prime numbers */
wps = [];
for(i = 1, +oo,
if(isprime(woodall(i)),
wps = concat(wps, i);
if(#wps >= 12, break);
);
);
print(wps);
}
</syntaxhighlight>
{{out}}
<pre>
[3, 9, 25, 65, 161, 385, 897, 2049, 4609, 10241, 22529, 49153, 106497, 229377, 491521, 1048577, 2228225, 4718593, 9961473, 20971521]
[1, 7, 23, 63, 159, 383, 895, 2047, 4607, 10239, 22527, 49151, 106495, 229375, 491519, 1048575, 2228223, 4718591, 9961471, 20971519]
[1, 141, 4713, 5795, 6611]
[2, 3, 6, 30, 75, 81, 115, 123, 249, 362, 384, 462]
</pre>
=={{header|Perl}}==
{{libheader|ntheory}}
<
use warnings;
use bigint;
Line 413 ⟶ 1,247:
($m,$n) = (12,0);
print "\n\nFirst $m Woodall primes: (in terms of n)\n";
print do { $n < $m ? (!!is_prime(cullen $_,-1) and ++$n and "$_ ") : last } for 1 .. Inf;</
{{out}}
<pre>First 20 Cullen numbers:
Line 426 ⟶ 1,260:
First 12 Woodall primes: (in terms of n)
2 3 6 30 75 81 115 123 249 362 384 462</pre>
=={{header|Phix}}==
<!--<
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
Line 476 ⟶ 1,311:
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"First 12 Woodall primes (in terms of n):%s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">w</span><span style="color: #0000FF;">)})</span>
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)</span>
<!--</
{{out}}
<pre>
Line 486 ⟶ 1,321:
</pre>
Note the time given is for desktop/Phix 64bit, for comparison the Julia entry took about 20s on the same box. On 32-bit it is nearly 5 times slower (2 minutes and 38s) and hence under pwa/p2js in a browser (which is inherently 32bit) it is limited to the first 2 cullen primes only, but manages that in 0.4s.
=={{header|Python}}==
<
print("working...")
print("First 20 Cullen numbers:")
for n in range(1,
num = n*pow(2,n)+1
print(str(num),end= " ")
Line 521 ⟶ 1,334:
print("First 20 Woodall numbers:")
for n in range(1,
num = n*pow(2,n)-1
print(str(num),end=" ")
Line 527 ⟶ 1,340:
print()
print("done...")
</syntaxhighlight>
{{out}}
<pre>
working...
First 20 Cullen numbers:
3 9 25 65 161 385 897 2049 4609 10241 22529 49153 106497 229377 491521 1048577 2228225 4718593 9961473 20971521
First 20 Woodall numbers:
1 7 23 63 159 383 895 2047 4607 10239 22527 49151 106495 229375 491519 1048575 2228223 4718591 9961471 20971519
done...
</pre>
===Bit Shift===
{{trans|Quackery}}
<syntaxhighlight lang="python">def cullen(n): return((n<<n)+1)
def woodall(n): return((n<<n)-1)
print("First 20 Cullen numbers:")
for i in range(1,21):
print(cullen(i),end=" ")
print()
print()
print("First 20 Woodall numbers:")
for i in range(1,21):
print(woodall(i),end=" ")
print()</syntaxhighlight>
{{out}}
Same as Quackery.
=={{header|Quackery}}==
<syntaxhighlight lang="quackery"> [ dup << 1+ ] is cullen ( n --> n )
[ dup << 1 - ] is woodall ( n --> n )
say "First 20 Cullen numbers:" cr
20 times [ i^ 1+ cullen echo sp ] cr
cr
say "First 20 Woodall numbers:" cr
20 times [ i^ 1+ woodall echo sp ] cr</syntaxhighlight>
{{out}}
<pre>First 20 Cullen numbers:
3 9 25 65 161 385 897 2049 4609 10241 22529 49153 106497 229377 491521 1048577 2228225 4718593 9961473 20971521
First 20 Woodall numbers:
1 7 23 63 159 383 895 2047 4607 10239 22527 49151 106495 229375 491519 1048575 2228223 4718591 9961471 20971519
</pre>
=={{header|Raku}}==
<syntaxhighlight lang="raku" line>my @cullen = ^∞ .map: { $_ × 1 +< $_ + 1 };
my @woodall = ^∞ .map: { $_ × 1 +< $_ - 1 };
put "First 20 Cullen numbers: ( n × 2**n + 1)\n", @cullen[1..20]; # A002064
put "\nFirst 20 Woodall numbers: ( n × 2**n - 1)\n", @woodall[1..20]; # A003261
put "\nFirst 5 Cullen primes: (in terms of n)\n", @cullen.grep( &is-prime, :k )[^5]; # A005849
put "\nFirst 12 Woodall primes: (in terms of n)\n", @woodall.grep( &is-prime, :k )[^12]; # A002234</syntaxhighlight>
{{out}}
<pre>First 20 Cullen numbers: ( n × 2**n + 1)
3 9 25 65 161 385 897 2049 4609 10241 22529 49153 106497 229377 491521 1048577 2228225 4718593 9961473 20971521
First 20 Woodall numbers: ( n × 2**n - 1)
1 7 23 63 159 383 895 2047 4607 10239 22527 49151 106495 229375 491519 1048575 2228223 4718591 9961471 20971519
First 5 Cullen primes: (in terms of n)
1 141 4713 5795 6611
First 12 Woodall primes: (in terms of n)
2 3 6 30 75 81 115 123 249 362 384 462</pre>
=={{header|Ring}}==
<
load "stdlib.ring"
Line 558 ⟶ 1,432:
see nl + "done..." + nl
</syntaxhighlight>
{{out}}
<pre>
Line 568 ⟶ 1,442:
1 7 23 63 159 383 895 2047 4607 10239 22527 49151 106495 229375 491519 1048575 2228223 4718591 9961471 20971519
done...
</pre>
=={{header|RPL}}==
≪ DUP R→B
1 ROT '''START''' SL '''NEXT'''
1 + B→R
≫ '<span style="color:blue">CULLIN</span>' STO
≪ <span style="color:blue">CULLIN</span> 2 -
≫ '<span style="color:blue">WDHAL</span>' STO
≪ {} 1 20 '''FOR''' n n <span style="color:blue">CULLIN</span> + '''NEXT''' ≫ EVAL
≪ {} 1 20 '''FOR''' n n <span style="color:blue">WDHAL</span> + '''NEXT''' ≫ EVAL
{{out}}
<pre>
2: { 3 9 25 65 161 385 897 2049 4609 10241 22529 49153 106497 229377 491521 1048577 2228225 4718593 9961473 20971521 }
1: { 1 7 23 63 159 383 895 2047 4607 10239 22527 49151 106495 229375 491519 1048575 2228223 4718591 9961471 20971519 }
</pre>
=={{header|Ruby}}==
The OpenSSL prime? methods is faster than the standard one. It still takes 1-2 minutes to calculate the first 5 Cullen primes.
<syntaxhighlight lang="ruby">require 'openssl'
cullen = Enumerator.new{|y| (1..).each{|n| y << (n*(1<<n) + 1)} }
woodall = Enumerator.new{|y| (1..).each{|n| y << (n*(1<<n) - 1)} }
cullen_primes = Enumerator.new{|y| (1..).each {|i|y << i if OpenSSL::BN.new(cullen.next).prime?}}
woodall_primes = Enumerator.new{|y| (1..).each{|i|y << i if OpenSSL::BN.new(woodall.next).prime?}}
num = 20
puts "First #{num} Cullen numbers:\n#{cullen.first(num).join(" ")}"
puts "First #{num} Woodal numbers:\n#{woodall.first(num).join(" ")}"
puts "First 5 Cullen primes:\n#{cullen_primes.first(5).join(", ")}"
puts "First 12 Woodall primes:\n#{woodall_primes.first(12).join(", ")}"
</syntaxhighlight>
{{out}}
<pre>First 20 Cullen numbers:
3 9 25 65 161 385 897 2049 4609 10241 22529 49153 106497 229377 491521 1048577 2228225 4718593 9961473 20971521
First 20 Woodal numbers:
1 7 23 63 159 383 895 2047 4607 10239 22527 49151 106495 229375 491519 1048575 2228223 4718591 9961471 20971519
First 5 Cullen primes:
1, 141, 4713, 5795, 6611
First 12 Woodall primes:
2, 3, 6, 30, 75, 81, 115, 123, 249, 362, 384, 462
</pre>
=={{header|Rust}}==
<syntaxhighlight lang="rust">// [dependencies]
// rug = "1.15.0"
use rug::integer::IsPrime;
use rug::Integer;
fn cullen_number(n: u32) -> Integer {
let num = Integer::from(n);
(num << n) + 1
}
fn woodall_number(n: u32) -> Integer {
let num = Integer::from(n);
(num << n) - 1
}
fn main() {
println!("First 20 Cullen numbers:");
let cullen: Vec<String> = (1..21).map(|x| cullen_number(x).to_string()).collect();
println!("{}", cullen.join(" "));
println!("\nFirst 20 Woodall numbers:");
let woodall: Vec<String> = (1..21).map(|x| woodall_number(x).to_string()).collect();
println!("{}", woodall.join(" "));
println!("\nFirst 5 Cullen primes in terms of n:");
let cullen_primes: Vec<String> = (1..)
.filter_map(|x| match cullen_number(x).is_probably_prime(25) {
IsPrime::No => None,
_ => Some(x.to_string()),
})
.take(5)
.collect();
println!("{}", cullen_primes.join(" "));
println!("\nFirst 12 Woodall primes in terms of n:");
let woodall_primes: Vec<String> = (1..)
.filter_map(|x| match woodall_number(x).is_probably_prime(25) {
IsPrime::No => None,
_ => Some(x.to_string()),
})
.take(12)
.collect();
println!("{}", woodall_primes.join(" "));
}</syntaxhighlight>
{{out}}
<pre>
First 20 Cullen numbers:
3 9 25 65 161 385 897 2049 4609 10241 22529 49153 106497 229377 491521 1048577 2228225 4718593 9961473 20971521
First 20 Woodall numbers:
1 7 23 63 159 383 895 2047 4607 10239 22527 49151 106495 229375 491519 1048575 2228223 4718591 9961471 20971519
First 5 Cullen primes in terms of n:
1 141 4713 5795 6611
First 12 Woodall primes in terms of n:
2 3 6 30 75 81 115 123 249 362 384 462
</pre>
=={{header|Scala}}==
{{trans|Java}}
<syntaxhighlight lang="Scala">
import java.math.BigInteger
import scala.annotation.tailrec
object CullenAndWoodhall extends App {
val Certainty = 20
var number: BigInteger = _
var power: BigInteger = _
var count: Int = _
var primeIndex: Int = _
sealed trait NumberType
case object Cullen extends NumberType
case object Woodhall extends NumberType
numberSequence(20, Cullen)
numberSequence(20, Woodhall)
primeSequence(5, Cullen)
primeSequence(12, Woodhall)
def numberSequence(aCount: Int, aNumberType: NumberType): Unit = {
println(s"\nThe first $aCount $aNumberType numbers are:")
numberInitialise()
(1 to aCount).foreach { _ =>
print(nextNumber(aNumberType).toString + " ")
}
println()
}
def primeSequence(aCount: Int, aNumberType: NumberType): Unit = {
println(s"\nThe indexes of the first $aCount $aNumberType primes are:")
primeInitialise()
@tailrec
def findPrimes(): Unit = {
if (count < aCount) {
if (nextNumber(aNumberType).isProbablePrime(Certainty)) {
print(primeIndex + " ")
count += 1
}
primeIndex += 1
findPrimes()
}
}
findPrimes()
println()
}
def nextNumber(aNumberType: NumberType): BigInteger = {
number = number.add(BigInteger.ONE)
power = power.shiftLeft(1)
aNumberType match {
case Cullen => number.multiply(power).add(BigInteger.ONE)
case Woodhall => number.multiply(power).subtract(BigInteger.ONE)
}
}
def numberInitialise(): Unit = {
number = BigInteger.ZERO
power = BigInteger.ONE
}
def primeInitialise(): Unit = {
count = 0
primeIndex = 1
numberInitialise()
}
}
</syntaxhighlight>
{{out}}
<pre>
The first 20 Cullen numbers are:
3 9 25 65 161 385 897 2049 4609 10241 22529 49153 106497 229377 491521 1048577 2228225 4718593 9961473 20971521
The first 20 Woodhall numbers are:
1 7 23 63 159 383 895 2047 4607 10239 22527 49151 106495 229375 491519 1048575 2228223 4718591 9961471 20971519
The indexes of the first 5 Cullen primes are:
1 141 4713 5794 6611
The indexes of the first 12 Woodhall primes are:
2 3 6 30 75 81 115 123 249 362 384 462
</pre>
=={{header|Sidef}}==
<
func woodall(n) { n * (1 << n) - 1 }
Line 584 ⟶ 1,654:
say "\nFirst 12 Woodall primes: (in terms of n)"
say 12.by { woodall(_).is_prime }.join(' ')</
{{out}}
<pre>
Line 601 ⟶ 1,671:
=={{header|Verilog}}==
<
integer n, num;
Line 620 ⟶ 1,690:
$finish ;
end
endmodule</
Line 627 ⟶ 1,697:
{{libheader|Wren-big}}
Cullen primes limited to first 2 as very slow after that.
<
var cullen = Fn.new { |n| (BigInt.one << n) * n + 1 }
Line 662 ⟶ 1,732:
n = n + 1
}
System.print()</
{{out}}
Line 682 ⟶ 1,752:
{{libheader|Wren-gmp}}
Cullen primes still slow to emerge, just over 10 seconds overall.
<
import "./gmp" for Mpz
Line 719 ⟶ 1,789:
n = n + 1
}
System.print()</
{{out}}
Line 734 ⟶ 1,804:
First 12 Woodall primes (in terms of n):
2 3 6 30 75 81 115 123 249 362 384 462
</pre>
=={{header|XPL0}}==
{{trans|11l}}
<syntaxhighlight lang "XPL0">func Cullen(N);
int N;
return N<<N + 1;
func Woodall(N);
int N;
return N<<N - 1;
int I;
[Text(0, "First 20 Cullen numbers:^m^j");
for I:= 1 to 20 do
[IntOut(0, Cullen(I)); ChOut(0, ^ )];
CrLf(0);
CrLf(0);
Text(0, "First 20 Woodall numbers:^m^j");
for I:= 1 to 20 do
[IntOut(0, Woodall(I)); ChOut(0, ^ )];
CrLf(0);
]</syntaxhighlight>
{{out}}
<pre>
First 20 Cullen numbers:
3 9 25 65 161 385 897 2049 4609 10241 22529 49153 106497 229377 491521 1048577 2228225 4718593 9961473 20971521
First 20 Woodall numbers:
1 7 23 63 159 383 895 2047 4607 10239 22527 49151 106495 229375 491519 1048575 2228223 4718591 9961471 20971519
</pre>
| |||