A236760 Numbers n such that n^4 + n +- 1 are twin primes.

2, 6, 9, 12, 26, 44, 72, 77, 119, 204, 266, 290, 351, 506, 539, 542, 561, 644, 741, 807, 861, 924, 992, 996, 1016, 1032, 1049, 1356, 1412, 1556, 1640, 1794, 1847, 1862, 1871, 1895, 1980, 2036, 2129, 2222, 2289, 2354, 2445, 2616, 2630

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

992^4 + 992 + 1 (968381957089) and 992^4 + 992 - 1 (968381957087) are twin primes. Thus, 992 is a member of this sequence.

Mathematica

Select[Range[3000], PrimeQ[#^4 + # - 1] && PrimeQ[#^4 + # + 1] &] (* Vincenzo Librandi, Dec 26 2015 *)
Select[Range[3000], AllTrue[#^4+#+{1, -1}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 13 2017 *)

Prog

(Python)
import sympy
from sympy import isprime
{print(n) for n in range(10**4) if isprime(n**4+n-1) and isprime(n**4+n+1)}
(PARI)
s=[]; for(n=1, 3000, if(isprime(n^4+n+1)&&isprime(n^4+n-+1), s=concat(s, n))); s \\ Colin Barker, Jan 31 2014
(Magma) [n: n in [1..5*10^3] |IsPrime(n^4+n-1) and IsPrime(n^4 +n+1)]; // Vincenzo Librandi, Dec 26 2015

Crossrefs

Intersection of A236759 and A049408.

Sequence in context: A293789 A112870 A169915 * A086562 A083789 A003145

Adjacent sequences: A236757 A236758 A236759 * A236761 A236762 A236763

Keyword

nonn,easy

Author

Derek Orr, Jan 30 2014

Status

approved