Jacobsthal numbers: Difference between revisions
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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>
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