A258805 -id:A258805 - cp's OEIS frontend

A006314 Numbers k such that k^8 + 1 is prime.

1, 2, 4, 118, 132, 140, 152, 208, 240, 242, 288, 290, 306, 378, 392, 426, 434, 442, 508, 510, 540, 542, 562, 596, 610, 664, 680, 682, 732, 782, 800, 808, 866, 876, 884, 892, 916, 918, 934, 956, 990, 1022, 1028, 1054, 1106, 1120, 1174, 1224, 1232, 1256, 1284

Offset: 1

N. J. A. Sloane

Dubner, Harvey. "Generalized Fermat primes." J. Recreational Math., 18 (1985): 279-280.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n=1..10000

Cf. A005574, A000068, A006313, A006315, A006316, A056994, A056995, A057465, A057002, A088361, A088362, A226528, A226529, A226530, A251597, A253854, A244150, A243959, A321323.

[n: n in [0..2000] | IsPrime(n^8+1)]; // Vincenzo Librandi, Nov 18 2010

Select[Range[1300],PrimeQ[#^8+1]&]  (* Harvey P. Dale, Mar 31 2011 *)

isA006314(n) = isprime(n^8+1) \\ Michael B. Porter, Mar 24 2010

A258805(n) = a(n)^8+1. - R. J. Mathar, Jun 05 2025

More terms from James Sellers, May 03 2000

A272137 Primes of the form k^16 + 1.

Original entry on oeis.org

2, 65537, 197352587024076973231046657, 808551180810136214718004658177, 1238846438084943599707227160577, 37157429083410091685945089785857, 123025056645280288014028950372089857, 150838912030874130174020868290707457

Offset: 1

Jaroslav Krizek, May 08 2016

nonn

Corresponding values of k are in A006313.

Jaroslav Krizek, Table of n, a(n) for n = 1..100

Cf. Sequences of numbers n such that n^(2^k)+1 is a prime p for k = 1-13: A005574 (k=1), A000068 (k=2), A006314 (k=3), A006313 (k=4), A006315 (k=5), A006316 (k=6), A056994 (k=7), A056995 (k=8), A057465 (k=9), A057002 (k=10), A088361 (k=11), A088362 (k=12), A226528 (k=13).

Corresponding sequences of primes p of the form n^(2^k)+1 for k = 1-4: A002496 (k=1), A037896 (k=2), A258805 (k=3), A272137 (k=4).

[n^16 + 1: n in [1..700] | IsPrime(n^16 + 1)];

A272137:=n->`if`(isprime(n^16+1), n^16+1, NULL): seq(A272137(n), n=1..200); # Wesley Ivan Hurt, May 11 2016

cp's OEIS Frontend

A006314 Numbers k such that k^8 + 1 is prime.

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