A217991 Numbers n such that n^16+1 and (n+2)^16+1 are both prime.

74, 156, 474, 476, 686, 688, 774, 776, 830, 832, 982, 2698, 3560, 3646, 4016, 5974, 8542, 8732, 10730, 10858, 12164, 12902, 13022, 13154, 13554, 13838, 13840, 20436, 20454, 20504, 21912, 24554, 24770, 25582, 30144, 31634, 31882, 32358, 32360, 32992, 33758

Offset

1,1

Links

Table of n, a(n) for n=1..41.

Example

74 is in the sequence because 74^16+1 =  808551180810136214718004658177 and 76^16+1 = 1238846438084943599707227160577 are both prime.

Mathematica

lst={}; Do[p=n^16+1; q=(n+2)^16+1; If[PrimeQ[p] && PrimeQ[q], AppendTo[lst, n]], {n, 0, 34000}]; lst
Select[Range[34000], AllTrue[{#^16+1, (#+2)^16+1}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jun 24 2015 *)

Crossrefs

Cf. A006313.

Sequence in context: A365201 A044325 A044706 * A105053 A260171 A044406

Adjacent sequences: A217988 A217989 A217990 * A217992 A217993 A217994

Keyword

nonn,easy

Author

Michel Lagneau, Oct 17 2012

Status

approved