Jacobsthal numbers: Difference between revisions
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Line 1,102:
5562466239377370006237035693149875298444543026970449921737087520370363869220418099018130434731
95562442332919646317117537304253622533190207882011713489066201641121786503686867002917439712921903606443
</pre>
=={{header|C#}}==
{{trans|Java}}
<syntaxhighlight lang="C#">
using System;
using System.Numerics;
using System.Threading;
public class JacobsthalNumbers
{
private static BigInteger currentJacobsthal = 0;
private static int latestIndex = 0;
private static readonly BigInteger Three = new BigInteger(3);
private const int Certainty = 20;
public static void Main(string[] args)
{
Console.WriteLine("The first 30 Jacobsthal Numbers:");
for (int i = 0; i < 6; i++)
{
for (int k = 0; k < 5; k++)
{
Console.Write($"{JacobsthalNumber(i * 5 + k), 15}");
}
Console.WriteLine();
}
Console.WriteLine();
Console.WriteLine("The first 30 Jacobsthal-Lucas Numbers:");
for (int i = 0; i < 6; i++)
{
for (int k = 0; k < 5; k++)
{
Console.Write($"{JacobsthalLucasNumber(i * 5 + k), 15}");
}
Console.WriteLine();
}
Console.WriteLine();
Console.WriteLine("The first 20 Jacobsthal oblong Numbers:");
for (int i = 0; i < 4; i++)
{
for (int k = 0; k < 5; k++)
{
Console.Write($"{JacobsthalOblongNumber(i * 5 + k), 15}");
}
Console.WriteLine();
}
Console.WriteLine();
Console.WriteLine("The first 10 Jacobsthal Primes:");
for (int i = 0; i < 10; i++)
{
Console.WriteLine(JacobsthalPrimeNumber());
}
}
private static BigInteger JacobsthalNumber(int index)
{
BigInteger value = new BigInteger(ParityValue(index));
return ((BigInteger.Parse("1") << index) - value) / Three;
}
private static long JacobsthalLucasNumber(int index)
{
return (1L << index) + ParityValue(index);
}
private static long JacobsthalOblongNumber(int index)
{
BigInteger nextJacobsthal = JacobsthalNumber(index + 1);
long result = (long)(currentJacobsthal * nextJacobsthal);
currentJacobsthal = nextJacobsthal;
return result;
}
private static long JacobsthalPrimeNumber()
{
BigInteger candidate = JacobsthalNumber(latestIndex++);
while (!candidate.IsProbablyPrime(Certainty))
{
candidate = JacobsthalNumber(latestIndex++);
}
return (long)candidate;
}
private static int ParityValue(int index)
{
return (index & 1) == 0 ? +1 : -1;
}
}
public static class BigIntegerExtensions
{
private static Random random = new Random();
public static bool IsProbablyPrime(this BigInteger source, int certainty)
{
if (source == 2 || source == 3)
return true;
if (source < 2 || source % 2 == 0)
return false;
BigInteger d = source - 1;
int s = 0;
while (d % 2 == 0)
{
d /= 2;
s += 1;
}
for (int i = 0; i < certainty; i++)
{
BigInteger a = RandomBigInteger(2, source - 2);
BigInteger x = BigInteger.ModPow(a, d, source);
if (x == 1 || x == source - 1)
continue;
for (int r = 1; r < s; r++)
{
x = BigInteger.ModPow(x, 2, source);
if (x == 1)
return false;
if (x == source - 1)
break;
}
if (x != source - 1)
return false;
}
return true;
}
private static BigInteger RandomBigInteger(BigInteger minValue, BigInteger maxValue)
{
if (minValue > maxValue)
throw new ArgumentException("minValue must be less than or equal to maxValue");
BigInteger range = maxValue - minValue + 1;
int length = range.ToByteArray().Length;
byte[] buffer = new byte[length];
BigInteger result;
do
{
random.NextBytes(buffer);
buffer[buffer.Length - 1] &= 0x7F; // Ensure non-negative
result = new BigInteger(buffer);
} while (result < minValue || result >= maxValue);
return result;
}
}
</syntaxhighlight>
{{out}}
<pre>
The first 30 Jacobsthal Numbers:
0 1 1 3 5
11 21 43 85 171
341 683 1365 2731 5461
10923 21845 43691 87381 174763
349525 699051 1398101 2796203 5592405
11184811 22369621 44739243 89478485 178956971
The first 30 Jacobsthal-Lucas Numbers:
2 1 5 7 17
31 65 127 257 511
1025 2047 4097 8191 16385
32767 65537 131071 262145 524287
1048577 2097151 4194305 8388607 16777217
33554431 67108865 134217727 268435457 536870911
The first 20 Jacobsthal oblong Numbers:
0 1 3 15 55
231 903 3655 14535 58311
232903 932295 3727815 14913991 59650503
238612935 954429895 3817763271 15270965703 61084037575
The first 10 Jacobsthal Primes:
3
5
11
43
683
2731
43691
174763
2796203
715827883
</pre>
Line 1,201 ⟶ 1,398:
95562442332919646317117537304253622533190207882011713489066201641121786503686867002917439712921903606443
</pre>
=={{header|Delphi}}==
{{works with|Delphi|6.0}}
{{libheader|SysUtils,StdCtrls}}
<syntaxhighlight lang="Delphi">
procedure GetJacobsthalNum(Lucas: boolean; Max: integer; var IA: TInt64DynArray);
{Get Jacobsthal number sequence. If Lucas is true do Lucal variation}
var I: integer;
begin
SetLength(IA,Max);
{Lucas starts sequence with 2 instead of 0}
if Lucas then IA[0]:=2 else IA[0]:=0;
IA[1]:=1;
{Calculate Nn = Nn-1 + 2 Nn-2}
for I:=2 to Max-1 do
IA[I]:=IA[I-1] + 2 * IA[I-2];
end;
procedure GetJacobsthalOblong(Max: integer; var IA: TInt64DynArray);
{Jacobsthal Oblong numbers is Nn = Jn x Jn=1 where J = Jacobsthal numbers}
var IA2: TInt64DynArray;
var I: integer;
begin
GetJacobsthalNum(False,Max+1,IA2);
SetLength(IA,Max);
for I:=0 to High(IA2)-1 do
begin
IA[I]:=IA2[I] * IA2[I+1];
end;
end;
procedure GetJacobsthalPrimes(Memo: TMemo);
var I: integer;
var Jacob,N1, N2: int64;
function GetNext: int64;
{Nn = Nn-1 + 2 x Nn-2}
begin
Result:=N1 + 2 * N2;
N2:=N1; N1:=Result;
end;
begin
N2:=0; N1:=1;
for I:=1 to 10 do
begin
repeat Jacob:=GetNext;
until IsPrime(Jacob);
Memo.Lines.Add(IntToStr(I)+' - '+IntToStr(Jacob));
end;
end;
procedure ShowJacobsthalNumbers(Memo: TMemo);
var I: integer;
var IA: TInt64DynArray;
var S: string;
begin
GetJacobsthalNum(False,30,IA);
Memo.Lines.Add('First 30 Jacobsthal Numbers');
S:='';
for I:=0 to High(IA) do
begin
S:=S+Format('%12.0n',[IA[I]+0.0]);
if (I mod 5)=4 then S:=S+CRLF;
end;
Memo.Lines.Add(S);
Memo.Lines.Add('');
GetJacobsthalNum(True,30,IA);
Memo.Lines.Add('First 30 Jacobsthal-Lucas Numbers');
S:='';
for I:=0 to High(IA) do
begin
S:=S+Format('%14.0n',[IA[I]+0.0]);
if (I mod 4)=3 then S:=S+CRLF;
end;
Memo.Lines.Add(S);
Memo.Lines.Add('');
GetJacobsthalOblong(20,IA);
Memo.Lines.Add('First 20 Jacobsthal-Oblong Numbers');
S:='';
for I:=0 to High(IA) do
begin
S:=S+Format('%18.0n',[IA[I]+0.0]);
if (I mod 3)=2 then S:=S+CRLF;
end;
Memo.Lines.Add(S);
Memo.Lines.Add('');
GetJacobsthalPrimes(Memo);
end;
</syntaxhighlight>
{{out}}
<pre>
First 30 Jacobsthal Numbers
0 1 1 3 5
11 21 43 85 171
341 683 1,365 2,731 5,461
10,923 21,845 43,691 87,381 174,763
349,525 699,051 1,398,101 2,796,203 5,592,405
11,184,811 22,369,621 44,739,243 89,478,485 178,956,971
First 30 Jacobsthal-Lucas Numbers
2 1 5 7
17 31 65 127
257 511 1,025 2,047
4,097 8,191 16,385 32,767
65,537 131,071 262,145 524,287
1,048,577 2,097,151 4,194,305 8,388,607
16,777,217 33,554,431 67,108,865 134,217,727
268,435,457 536,870,911
First 20 Jacobsthal-Oblong Numbers
0 1 3
15 55 231
903 3,655 14,535
58,311 232,903 932,295
3,727,815 14,913,991 59,650,503
238,612,935 954,429,895 3,817,763,271
15,270,965,703 61,084,037,575
1 - 3
2 - 5
3 - 11
4 - 43
5 - 683
6 - 2731
7 - 43691
8 - 174763
9 - 2796203
10 - 715827883
Elapsed Time: 49.627 ms.
</pre>
=={{header|F Sharp|F#}}==
<syntaxhighlight lang="fsharp">
Line 1,380 ⟶ 1,726:
2796203
715827883</pre>
=={{header|Gambas}}==
<syntaxhighlight lang="vbnet">Public n As New Long[2]
Public Sub Main()
Dim i0 As Integer = 0, i1 As Integer = 1
Dim j As Integer, c As Integer, P As Integer = 1, Q As Integer = -2
Print "First 30 Jacobsthal numbers:"
c = 0
n[i0] = 0
n[i1] = 1
For j = 0 To 29
c += 1
Print Format$(n[i0], " #########");
If (c Mod 5) Then
Print "";
Else
Print Chr(10);
End If
n[i0] = P * n[i1] - Q * n[i0]
Swap i0, i1
Next
Print "\n\nFirst 30 Jacobsthal-Lucas numbers: "
c = 0
n[i0] = 2
n[i1] = 1
For j = 0 To 29
c += 1
Print Format$(n[i0], " #########");
If (c Mod 5) Then
Print "";
Else
Print Chr(10);
End If
n[i0] = P * n[i1] - Q * n[i0]
Swap i0, i1
Next
Print "\n\nFirst 20 Jacobsthal oblong numbers: "
c = 0
n[i0] = 0
n[i1] = 1
For j = 0 To 19
c += 1
Print Format$(n[i0] * n[i1], " ###########");
If (c Mod 5) Then
Print "";
Else
Print Chr(10);
End If
n[i0] = P * n[i1] - Q * n[i0]
Swap i0, i1
Next
Print "\n\nFirst 10 Jacobsthal primes: "
c = 0
n[i0] = 0
n[i1] = 1
Do
If isPrime(n[i0]) Then
c += 1
Print n[i0]
End If
n[i0] = P * n[i1] - Q * n[i0]
Swap i0, i1
Loop Until c = 10
End
Public Sub isPrime(ValorEval As Long) As Boolean
If ValorEval < 2 Then Return False
If ValorEval Mod 2 = 0 Then Return ValorEval = 2
If ValorEval Mod 3 = 0 Then Return ValorEval = 3
Dim d As Long = 5
While d * d <= ValorEval
If ValorEval Mod d = 0 Then Return False Else d += 2
Wend
Return True
End Function </syntaxhighlight>
{{out}}
<pre>Same as FreeBASIC entry.</pre>
=={{header|Go}}==
Line 1,638 ⟶ 2,070:
ja I.1 p:ja i.32 NB. first ten Jacobsthal primes
3 5 11 43 683 2731 43691 174763 2796203 715827883</syntaxhighlight>
=={{header|Java}}==
<syntaxhighlight lang="java">
import java.math.BigInteger;
public final class JacobsthalNumbers {
public static void main(String[] aArgs) {
System.out.println("The first 30 Jacobsthal Numbers:");
for ( int i = 0; i < 6; i++ ) {
for ( int k = 0; k < 5; k++ ) {
System.out.print(String.format("%15s", jacobsthalNumber(i * 5 + k)));
}
System.out.println();
}
System.out.println();
System.out.println("The first 30 Jacobsthal-Lucas Numbers:");
for ( int i = 0; i < 6; i++ ) {
for ( int k = 0; k < 5; k++ ) {
System.out.print(String.format("%15s", jacobsthalLucasNumber(i * 5 + k)));
}
System.out.println();
}
System.out.println();
System.out.println("The first 20 Jacobsthal oblong Numbers:");
for ( int i = 0; i < 4; i++ ) {
for ( int k = 0; k < 5; k++ ) {
System.out.print(String.format("%15s", jacobsthalOblongNumber(i * 5 + k)));
}
System.out.println();
}
System.out.println();
System.out.println("The first 10 Jacobsthal Primes:");
for ( int i = 0; i < 10; i++ ) {
System.out.println(jacobsthalPrimeNumber(i));
}
}
private static BigInteger jacobsthalNumber(int aIndex) {
BigInteger value = BigInteger.valueOf(parityValue(aIndex));
return BigInteger.ONE.shiftLeft(aIndex).subtract(value).divide(THREE);
}
private static long jacobsthalLucasNumber(int aIndex) {
return ( 1 << aIndex ) + parityValue(aIndex);
}
private static long jacobsthalOblongNumber(int aIndex) {
long nextJacobsthal = jacobsthalNumber(aIndex + 1).longValueExact();
long result = currentJacobsthal * nextJacobsthal;
currentJacobsthal = nextJacobsthal;
return result;
}
private static long jacobsthalPrimeNumber(int aIndex) {
BigInteger candidate = jacobsthalNumber(latestIndex++);
while ( ! candidate.isProbablePrime(CERTAINTY) ) {
candidate = jacobsthalNumber(latestIndex++);
}
return candidate.longValueExact();
}
private static int parityValue(int aIndex) {
return ( aIndex & 1 ) == 0 ? +1 : -1;
}
private static long currentJacobsthal = 0;
private static int latestIndex = 0;
private static final BigInteger THREE = BigInteger.valueOf(3);
private static final int CERTAINTY = 20;
}
</syntaxhighlight>
{{ out }}
<pre>
The first 30 Jacobsthal Numbers:
0 1 1 3 5
11 21 43 85 171
341 683 1365 2731 5461
10923 21845 43691 87381 174763
349525 699051 1398101 2796203 5592405
11184811 22369621 44739243 89478485 178956971
The first 30 Jacobsthal-Lucas Numbers:
2 1 5 7 17
31 65 127 257 511
1025 2047 4097 8191 16385
32767 65537 131071 262145 524287
1048577 2097151 4194305 8388607 16777217
33554431 67108865 134217727 268435457 536870911
The first 20 Jacobsthal oblong Numbers:
0 1 3 15 55
231 903 3655 14535 58311
232903 932295 3727815 14913991 59650503
238612935 954429895 3817763271 15270965703 61084037575
The first 10 Jacobsthal Primes:
3
5
11
43
683
2731
43691
174763
2796203
715827883
</pre>
=={{header|jq}}==
Line 1,843 ⟶ 2,388:
313 5562466239377370006237035693149875298444543026970449921737087520370363869220418099018130434731
347 95562442332919646317117537304253622533190207882011713489066201641121786503686867002917439712921903606443</pre>
=={{header|Maxima}}==
<syntaxhighlight lang="maxima">
jacobstahl(n):=(2^n-(-1)^n)/3$
jacobstahl_lucas(n):=2^n+(-1)^n$
jacobstahl_oblong(n):=jacobstahl(n)*jacobstahl(n+1)$
/* Function that returns a list of the first len jacobstahl primes */
jacobstahl_primes_count(len):=block(
[i:0,count:0,result:[]],
while count<len do (if primep(jacobstahl(i)) then (result:endcons(jacobstahl(i),result),count:count+1),i:i+1),
result)$
/* Test cases */
makelist(jacobstahl(i),i,0,29);
makelist(jacobstahl_lucas(i),i,0,29);
makelist(jacobstahl_oblong(i),i,0,19);
jacobstahl_primes_count(10);
</syntaxhighlight>
{{out}}
<pre>
[0,1,1,3,5,11,21,43,85,171,341,683,1365,2731,5461,10923,21845,43691,87381,174763,349525,699051,1398101,2796203,5592405,11184811,22369621,44739243,89478485,178956971]
[2,1,5,7,17,31,65,127,257,511,1025,2047,4097,8191,16385,32767,65537,131071,262145,524287,1048577,2097151,4194305,8388607,16777217,33554431,67108865,134217727,268435457,536870911]
[0,1,3,15,55,231,903,3655,14535,58311,232903,932295,3727815,14913991,59650503,238612935,954429895,3817763271,15270965703,61084037575]
[3,5,11,43,683,2731,43691,174763,2796203,715827883]
</pre>
=={{header|Nim}}==
<syntaxhighlight lang="Nim">import std/strutils
func isPrime(n: Natural): bool =
## Return true if "n" is prime.
if n < 2: return false
if n mod 2 == 0: return n == 2
if n mod 3 == 0: return n == 3
var step = 2
var d = 5
while d * d <= n:
if n mod d == 0: return false
inc d, step
step = 6 - step
result = true
iterator jacobsthalSequence(first, second: int): int =
## Yield the successive Jacobsthal numbers or
## Jacobsthal-Lucas numbers.
var prev = first
var curr = second
yield prev
yield curr
while true:
swap prev, curr
curr += curr + prev
yield curr
iterator jacobsthalOblong(): int =
## Yield the successive Jacobsthal oblong numbers.
var prev = -1
for n in jacobsthalSequence(0, 1):
if prev >= 0:
yield prev * n
prev = n
iterator jacobsthalPrimes(): int =
## Yield the successive Jacobsthal prime numbers.
for n in jacobsthalSequence(0, 1):
if n.isPrime:
yield n
echo "First 30 Jacobsthal numbers:"
var count = 0
for n in jacobsthalSequence(0, 1):
inc count
stdout.write align($n, 11)
if count mod 6 == 0: echo()
if count == 30: break
echo "\nFirst 30 Jacobsthal-Lucas numbers:"
count = 0
for n in jacobsthalSequence(2, 1):
inc count
stdout.write align($n, 11)
if count mod 6 == 0: echo()
if count == 30: break
echo "\nFirst 20 Jacobsthal oblong numbers:"
count = 0
for n in jacobsthalOblong():
inc count
stdout.write align($n, 13)
if count mod 5 == 0: echo()
if count == 20: break
echo "\nFirst 10 Jacobsthal prime numbers:"
count = 0
for n in jacobsthalPrimes():
inc count
stdout.write align($n, 11)
if count mod 5 == 0: echo()
if count == 10: break
</syntaxhighlight>
{{out}}
<pre>First 30 Jacobsthal numbers:
0 1 1 3 5 11
21 43 85 171 341 683
1365 2731 5461 10923 21845 43691
87381 174763 349525 699051 1398101 2796203
5592405 11184811 22369621 44739243 89478485 178956971
First 30 Jacobsthal-Lucas numbers:
2 1 5 7 17 31
65 127 257 511 1025 2047
4097 8191 16385 32767 65537 131071
262145 524287 1048577 2097151 4194305 8388607
16777217 33554431 67108865 134217727 268435457 536870911
First 20 Jacobsthal oblong numbers:
0 1 3 15 55
231 903 3655 14535 58311
232903 932295 3727815 14913991 59650503
238612935 954429895 3817763271 15270965703 61084037575
First 10 Jacobsthal prime numbers:
3 5 11 43 683
2731 43691 174763 2796203 715827883
</pre>
=={{header|OCaml}}==
Line 1,882 ⟶ 2,558:
First 10 Jacobsthal prime numbers:
3 5 11 43 683 2731 43691 174763 2796203 715827883
</pre>
=={{header|PARI/GP}}==
<syntaxhighlight lang="PARI/GP">
\\ Define the Jacobsthal function
Jacobsthal(n) = (2^n - (-1)^n) / 3;
\\ Define the JacobsthalLucas function
JacobsthalLucas(n) = 2^n + (-1)^n;
\\ Define the JacobsthalOblong function
JacobsthalOblong(n) = Jacobsthal(n) * Jacobsthal(n + 1);
{
\\ Generate and print Jacobsthal numbers for 0 through 29
print(vector(30, n, Jacobsthal(n-1)));
\\ Generate and print JacobsthalLucas numbers for 0 through 29
print(vector(30, n, JacobsthalLucas(n-1)));
\\ Generate and print JacobsthalOblong numbers for 0 through 19
print(vector(20, n, JacobsthalOblong(n-1)));
\\ Find the first 20 prime numbers in the Jacobsthal sequence
myprimes = [];
i = 0;
while(#myprimes < 40,
if(isprime(Jacobsthal(i)), myprimes = concat(myprimes, [i, Jacobsthal(i)]));
i++;
);
for (i = 1, #myprimes\2, print(myprimes[2*i-1] " " myprimes[2*i]); );
}
</syntaxhighlight>
{{out}}
<pre>
[0, 1, 1, 3, 5, 11, 21, 43, 85, 171, 341, 683, 1365, 2731, 5461, 10923, 21845, 43691, 87381, 174763, 349525, 699051, 1398101, 2796203, 5592405, 11184811, 22369621, 44739243, 89478485, 178956971]
[2, 1, 5, 7, 17, 31, 65, 127, 257, 511, 1025, 2047, 4097, 8191, 16385, 32767, 65537, 131071, 262145, 524287, 1048577, 2097151, 4194305, 8388607, 16777217, 33554431, 67108865, 134217727, 268435457, 536870911]
[0, 1, 3, 15, 55, 231, 903, 3655, 14535, 58311, 232903, 932295, 3727815, 14913991, 59650503, 238612935, 954429895, 3817763271, 15270965703, 61084037575]
3 3
4 5
5 11
7 43
11 683
13 2731
17 43691
19 174763
23 2796203
31 715827883
43 2932031007403
61 768614336404564651
79 201487636602438195784363
101 845100400152152934331135470251
127 56713727820156410577229101238628035243
167 62357403192785191176690552862561408838653121833643
191 1046183622564446793972631570534611069350392574077339085483
199 267823007376498379256993682056860433753700498963798805883563
313 5562466239377370006237035693149875298444543026970449921737087520370363869220418099018130434731
347 95562442332919646317117537304253622533190207882011713489066201641121786503686867002917439712921903606443
</pre>
Line 1,967 ⟶ 2,704:
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<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 30 Jacobsthal numbers:\n%s\n"</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">jba</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%9d"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">29</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">),</span><span style="color: #000000;">jacobsthal</span><span style="color: #0000FF;">)))</span>
<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 30 Jacobsthal-Lucas numbers:\n%s\n"</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">jba</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%9d"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">29</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">),</span><span style="color: #000000;">jacobsthal_lucas</span><span style="color: #0000FF;">)))</span>
<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 20 Jacobsthal oblong numbers:\n%s\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">jba</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%11d"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">19</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">),</span><span style="color: #000000;">jacobsthal_oblong</span><span style="color: #0000FF;">)))</span>
<span style="color: #000080;font-style:italic;">--printf(1,"First 10 Jacobsthal primes:\n%s\n", jba("%d",filter(apply(tagset(31,0),jacobsthal),is_prime),1))
--hmm(""), fine, but to go further roll out gmp:</span>
<span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
Line 2,534 ⟶ 3,274:
===Testing program===
≪ → func count
≪ { } 0
'''IF''' EVAL '''THEN''' ROT SWAP + SWAP '''ELSE''' DROP '''END'''
'''UNTIL''' OVER SIZE count ≥ '''END'''
DROP
≫ ≫
'<span style="color:blue">ASSRT</span>' STO
≪ <span style="color:blue">JCBN</span> 1 ≫ 30 <span style="color:blue">ASSRT</span>
≪ <span style="color:blue">JCBL</span> 1 ≫ 30 <span style="color:blue">ASSRT</span>
≪ <span style="color:blue">JCBO </span>1 ≫ 20 <span style="color:blue">ASSRT</span>
≪ DUP <span style="color:blue">JCBN PRIM?</span> ≫ 10 <span style="color:blue">ASSRT</span>
{{works with|Halcyon Calc|4.2.7}}
{{out}}
Line 2,688 ⟶ 3,429:
95562442332919646317117537304253622533190207882011713489066201641121786503686867002917439712921903606443
</pre>
=={{header|SETL}}==
<syntaxhighlight lang="setl">program jacobsthal_numbers;
print("First 30 Jacobsthal numbers:");
printseq([j n : n in [0..29]]);
print;
print("First 30 Jacobsthal-Lucas numbers:");
printseq([jl n : n in [0..29]]);
print;
print("First 20 Jacobsthal oblong numbers:");
printseq([jo n : n in [0..19]]);
print;
print("First 10 Jacobsthal primes:");
printseq([j n : n in [0..31] | prime j n]);
proc printseq(seq);
loop for n in seq do
nprint(lpad(str n, 14));
if (i +:= 1) mod 5 = 0 then print; end if;
end loop;
end proc;
op j(n);
return (2**n - (-1)**n) div 3;
end op;
op jl(n);
return 2**n + (-1)**n;
end op;
op jo(n);
return j n * j (n+1);
end op;
op prime(n);
if n<=4 then return n in {2,3}; end if;
return not exists d in [2..floor sqrt n] | n mod d = 0;
end op;
end program;</syntaxhighlight>
{{out}}
<pre>First 30 Jacobsthal numbers:
0 1 1 3 5
11 21 43 85 171
341 683 1365 2731 5461
10923 21845 43691 87381 174763
349525 699051 1398101 2796203 5592405
11184811 22369621 44739243 89478485 178956971
First 30 Jacobsthal-Lucas numbers:
2 1 5 7 17
31 65 127 257 511
1025 2047 4097 8191 16385
32767 65537 131071 262145 524287
1048577 2097151 4194305 8388607 16777217
33554431 67108865 134217727 268435457 536870911
First 20 Jacobsthal oblong numbers:
0 1 3 15 55
231 903 3655 14535 58311
232903 932295 3727815 14913991 59650503
238612935 954429895 3817763271 15270965703 61084037575
First 10 Jacobsthal primes:
3 5 11 43 683
2731 43691 174763 2796203 715827883</pre>
=={{header|Sidef}}==
Line 2,724 ⟶ 3,533:
[3, 5, 11, 43, 683, 2731, 43691, 174763, 2796203, 715827883, 2932031007403, 768614336404564651, 201487636602438195784363, 845100400152152934331135470251, 56713727820156410577229101238628035243, 62357403192785191176690552862561408838653121833643, 1046183622564446793972631570534611069350392574077339085483, 267823007376498379256993682056860433753700498963798805883563, 5562466239377370006237035693149875298444543026970449921737087520370363869220418099018130434731, 95562442332919646317117537304253622533190207882011713489066201641121786503686867002917439712921903606443]
</pre>
=={{header|uBasic/4tH}}==
{{trans|FreeBASIC}}
<syntaxhighlight lang="uBasic/4tH">Dim @n(2)
x = 0
y = 1
p = 1
q = -2
Print "First 30 Jacobsthal numbers:"
c = 0 : @n(x) = 0: @n(y) = 1
For j = 0 To 29
c = c + 1
Print Using " ____________#"; @n(x);
If (c % 5) = 0 Then Print
@n(x) = P * @n(y) - Q * @n(x)
Push x : x = y : y = Pop()
Next
Print : Print "First 30 Jacobsthal-Lucas numbers: "
c = 0 : @n(x) = 2: @n(y) = 1
For j = 0 To 29
c = c + 1
Print Using " ____________#"; @n(x);
If (c % 5) = 0 Then Print
@n(x) = P * @n(y) - Q * @n(x)
Push x : x = y : y = Pop()
Next
Print : Print "First 20 Jacobsthal oblong numbers: "
c = 0 : @n(x) = 0: @n(y) = 1
For j = 0 To 19
c = c + 1
Print Using " ____________#"; @n(x)*@n(y);
If (c % 5) = 0 Then Print
@n(x) = P * @n(y) - Q * @n(x)
Push x : x = y : y = Pop()
Next
Print : Print "First 10 Jacobsthal primes: "
c = 0 : @n(x) = 0 : @n(y) = 1
Do
If FUNC(_isPrime(@n(x))) Then c = c + 1 : Print @n(x)
@n(x) = P * @n(y) - Q * @n(x)
Push x : x = y : y = Pop()
Until c = 10
Loop
End
_isPrime
Param (1)
Local (1)
If (a@ < 2) Then Return (0)
If (a@ % 2) = 0 Then Return (0)
For b@ = 3 To Func(_Sqrt(a@, 0))+1 Step 2
If (a@ % b@) = 0 Then Unloop : Return (0)
Next
Return (1)
_Sqrt
Param (2)
Local (2)
If a@ = 0 Return (0)
c@ = Max(Shl(Set(a@, a@*(10^(b@*2))), -10), 1024)
Do
d@ = (c@+a@/c@)/2
While (c@ > d@)
c@ = d@
Loop
Return (c@)</syntaxhighlight>
{{Out}}
<pre>First 30 Jacobsthal numbers:
0 1 1 3 5
11 21 43 85 171
341 683 1365 2731 5461
10923 21845 43691 87381 174763
349525 699051 1398101 2796203 5592405
11184811 22369621 44739243 89478485 178956971
First 30 Jacobsthal-Lucas numbers:
2 1 5 7 17
31 65 127 257 511
1025 2047 4097 8191 16385
32767 65537 131071 262145 524287
1048577 2097151 4194305 8388607 16777217
33554431 67108865 134217727 268435457 536870911
First 20 Jacobsthal oblong numbers:
0 1 3 15 55
231 903 3655 14535 58311
232903 932295 3727815 14913991 59650503
238612935 954429895 3817763271 15270965703 61084037575
First 10 Jacobsthal primes:
3
5
11
43
683
2731
43691
174763
2796203
715827883
0 OK, 0:1024 </pre>
=={{header|V (Vlang)}}==
Line 2,818 ⟶ 3,737:
{{libheader|Wren-seq}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="
import "./seq" for Lst
import "./fmt" for Fmt
Line 2,828 ⟶ 3,747:
System.print("First 30 Jacobsthal numbers:")
var js = (0..29).map { |i| jacobsthal.call(i) }.toList
System.print("\nFirst 30 Jacobsthal-Lucas numbers:")
var jsl = (0..29).map { |i| jacobsthalLucas.call(i) }.toList
System.print("\nFirst 20 Jacobsthal oblong numbers:")
var oblongs = (0..19).map { |i| js[i] * js[i+1] }.toList
var primes = js.where { |j| j.isProbablePrime(10) }.toList
| |||