A121978 Numbers k such that (2*k^2)^8 + 1 is prime.

1, 11, 12, 14, 20, 27, 29, 30, 40, 65, 71, 85, 87, 89, 97, 104, 115, 147, 155, 175, 181, 189, 194, 244, 263, 264, 285, 286, 291, 303, 354, 360, 370, 376, 403, 407, 417, 423, 429, 433, 448, 479, 492, 493, 520, 570, 582, 588, 596, 617, 627, 629, 644, 654, 661

Offset: 1

Author

Alexander Adamchuk, Sep 10 2006

Keywords

• nonn
• easy
• changed

Comments

Corresponding primes of the form (2*k^2)^8 + 1 are {257, 11763130845074473217, 47330370277129322497, 557556054479199010817, 167772160000000000000001, ...}.

There are consecutive twin pairs {a(n),a(n+1)} = {11,12}, {29,30}, {263,264},{285,286}, {492,493}, {833,834}, ...

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A006314.

Programs

Mathematica

Select[Range[1000],PrimeQ[(2*#1^2)^8+1]&]
Select[Range[1000],PrimeQ[256#^16+1]&] (* Harvey P. Dale, Nov 04 2020 *)

PARI

is(n)=isprime((2*n^2)^8+1) \\ Charles R Greathouse IV, Jun 13 2017