A217972 Numbers n such that n^8 + 1 and (n + 2)^8 + 1 are both prime.

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

Offset: 1

Author

Michel Lagneau, Oct 17 2012

Keywords

• nonn
• easy

Examples

			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.
		

Crossrefs

Cf. A006314.

Programs

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 *)