%I #5 Oct 22 2012 18:24:05
%S 19,8,15,6,10,33,4,107,43,170,194,21,86,10,109,6,31,227,212,108,75,5,
%T 13,21,36,516,119,68,69,264,281,634,186,214,210,50,397,277,227,112,
%U 461,329,47,1399,257,231,131,68,530,981,242,298,219,508,196,266,97,234
%N a(n) is the smallest positive integer k such that k^16 + 1 == 0 mod p, where p is the n-th prime of the form 1 + 32*b (see A133870(n)).
%C A133870(n) : primes of form 32n+1.
%e a(5) = 10 because 10^16+1 = 10000000000000001 = 353 * 449 * 641 * 1409 * 69857 with A133870(5) = 449.
%t aa = {}; Do[p = Prime[n]; If[Mod[p, 32] == 1, k = 1; While[ ! Mod[k^16 + 1, p] == 0, k++ ]; AppendTo[aa, k]], {n, 300}]; aa
%Y Cf. A133870.
%K nonn
%O 1,1
%A _Michel Lagneau_, Oct 22 2012