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Primes of the form n^16 + 1.
1

%I #9 Sep 08 2022 08:46:16

%S 2,65537,197352587024076973231046657,808551180810136214718004658177,

%T 1238846438084943599707227160577,37157429083410091685945089785857,

%U 123025056645280288014028950372089857,150838912030874130174020868290707457

%N Primes of the form n^16 + 1.

%C Corresponding values of n are in A006313.

%H Jaroslav Krizek, <a href="/A272137/b272137.txt">Table of n, a(n) for n = 1..100</a>

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

%o (Magma) [n^16 + 1: n in [1..700] | IsPrime(n^16 + 1)]

%Y 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).

%Y 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).

%K nonn

%O 1,1

%A _Jaroslav Krizek_, May 08 2016