A217796 Primes of the form n^4+1 such that (n+2)^4+1 is also prime.

17, 257, 4477457, 8503057, 40960001, 59969537, 384160001, 5802782977, 58594980097, 94197431057, 102627966737, 114733948177, 283982410001, 330123790097, 381671897617, 405519334417, 691798081537, 741637881857, 1700843738897, 1749006250001, 2073600000001

Offset

1,1

Comments

The corresponding n are in A217795.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Example

257 is in the sequence because  4^4+1 = 257 and (4+2)^4+1 = 1297 are both prime.

Maple

for n from 0 by 2 to 3500 do: if type(n^4+1, prime)=true and type((n+2)^4+1, prime)=true then printf(`%d, `, n^4+1):else fi:od:

Mathematica

lst={}; Do[p=n^4+1; q=(n+2)^4+1; If[PrimeQ[p] && PrimeQ[q], AppendTo[lst, p]], {n, 0, 3500}]; lst
Select[Partition[Table[n^4+1, {n, 1300}], 3, 1], AllTrue[{#[[1]], #[[3]]}, PrimeQ]&][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 17 2020 *)

Crossrefs

Cf. A000068, A002523, A037896, A217795.

Sequence in context: A260407 A193329 A256499 * A014898 A048446 A001282

Adjacent sequences: A217793 A217794 A217795 * A217797 A217798 A217799

Keyword

nonn

Author

Michel Lagneau, Oct 12 2012

Status

approved