A217796 - OEIS

A217796

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

%I #11 Aug 17 2020 14:41:33

%S 17,257,4477457,8503057,40960001,59969537,384160001,5802782977,

%T 58594980097,94197431057,102627966737,114733948177,283982410001,

%U 330123790097,381671897617,405519334417,691798081537,741637881857,1700843738897,1749006250001,2073600000001

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

%C The corresponding n are in A217795.

%H Vincenzo Librandi, <a href="/A217796/b217796.txt">Table of n, a(n) for n = 1..1000</a>

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

%p 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:

%t lst={}; Do[p=n^4+1; q=(n+2)^4+1;If[PrimeQ[p] && PrimeQ[q], AppendTo[lst, p]], {n, 0, 3500}];lst

%t 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 *)

%Y Cf. A000068, A002523, A037896, A217795.

%K nonn

%O 1,1

%A _Michel Lagneau_, Oct 12 2012