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A217972 Numbers n such that n^8 + 1 and (n + 2)^8 + 1 are both prime. 0
2, 240, 288, 508, 540, 680, 916, 1614, 2328, 2872, 2960, 2988, 3402, 3708, 3770, 4760, 4762, 4810, 5370, 5490, 5776, 5878, 6204, 7276, 7890, 8414, 8652, 9418, 9858, 11218, 11896, 12510, 13328, 13938, 14418, 15846, 16422, 17206, 18152, 18954, 19226, 20640 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..42.

EXAMPLE

2 is in the sequence because 2^8 + 1 = 257 and 4^8 + 1 = 65537 are both prime.

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.

MATHEMATICA

lst = {}; Do[p = n^8 + 1; q = (n + 2)^8 + 1; If[PrimeQ[p] && PrimeQ[q], AppendTo[lst, n]], {n, 0, 21000}]; lst (* Lagneau *)

Select[Range[10^5], PrimeQ[#^8 + 1] && PrimeQ[(# + 2)^8 + 1] &] (* Alonso del Arte, Oct 17 2012 *)

CROSSREFS

Cf. A006314.

Sequence in context: A212839 A225784 A087226 * A071967 A024348 A006523

Adjacent sequences:  A217969 A217970 A217971 * A217973 A217974 A217975

KEYWORD

nonn,easy

AUTHOR

Michel Lagneau, Oct 17 2012

STATUS

approved

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Last modified May 9 17:41 EDT 2021. Contains 343742 sequences. (Running on oeis4.)