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%I #17 Oct 17 2012 19:46:51
%S 2,240,288,508,540,680,916,1614,2328,2872,2960,2988,3402,3708,3770,
%T 4760,4762,4810,5370,5490,5776,5878,6204,7276,7890,8414,8652,9418,
%U 9858,11218,11896,12510,13328,13938,14418,15846,16422,17206,18152,18954,19226,20640
%N Numbers n such that n^8 + 1 and (n + 2)^8 + 1 are both prime.
%e 2 is in the sequence because 2^8 + 1 = 257 and 4^8 + 1 = 65537 are both prime.
%e 4 is not in the sequence because although 4^8 + 1 is a prime (as we saw above), 6^8 + 1 is not, being a multiple of 17.
%t lst = {}; Do[p = n^8 + 1; q = (n + 2)^8 + 1; If[PrimeQ[p] && PrimeQ[q], AppendTo[lst, n]], {n, 0, 21000}]; lst (* Lagneau *)
%t Select[Range[10^5], PrimeQ[#^8 + 1] && PrimeQ[(# + 2)^8 + 1] &] (* _Alonso del Arte_, Oct 17 2012 *)
%Y Cf. A006314.
%K nonn,easy
%O 1,1
%A _Michel Lagneau_, Oct 17 2012
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