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%I #18 Sep 08 2022 08:46:10
%S 257,337,881,1217,1249,1553,1777,2113,2593,2657,2833,4049,4177,4273,
%T 4481,4513,4721,4993,5297,6353,6449,6481,6529,6689,7121,7489,8081,
%U 8609,9137,9281,9649,10177,10337,10369,10433,10657,11329,11617,11633,12049,12241,12577
%N Primes p congruent to 1 mod 16 such that x^8 = 2 has a solution mod p.
%C For a prime p congruent to 1 mod 16, the number 2 is an octavic residue mod p if and only if there are integers x and y such that x^2 + 256*y^2 = p.
%H Arkadiusz Wesolowski, <a href="/A252279/b252279.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Pri#smp">Index entries for related sequences</a>
%o (Magma) [p: p in PrimesUpTo(12577) | p mod 16 eq 1 and exists(t){x : x in ResidueClassRing(p) | x^8 eq 2}]; // _Arkadiusz Wesolowski_, Dec 19 2020
%o (PARI) isok(p) = isprime(p) && (Mod(p, 16) == 1) && ispower(Mod(2, p), 8); \\ _Michel Marcus_, Dec 19 2020
%Y Subsequence of A045315.
%K nonn
%O 1,1
%A _Arkadiusz Wesolowski_, Dec 16 2014
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