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A218165 a(n) is the smallest positive integer k such that k^128 + 1 == 0 mod p, where p is the n-th prime of the form 1 + 256*b (see A208178).

%I A218165 #5 Oct 22 2012 18:30:26
%S A218165 3,7,17,198,71,88,29,50,9,225,26,141,10,79,36,89,281,108,43,233,156,
%T A218165 412,430,296,79,20,76,178,80,54,1018,82,89,403,85,208,914,373,1226,62,
%U A218165 192,68,390,1055,1500,137,1018,141,95,54,160,52,11,754,674,182,517
%N A218165 a(n) is the smallest positive integer k such that k^128 + 1 == 0 mod p, where p is the n-th prime of the form 1 + 256*b (see A208178).
%C A218165 A208178(n): primes of form 256n+1.
%e A218165 a(1) = 3 because 3^128+1 = 2
%e A218165 * 257 * 275201 * 138424618868737 * 3913786281514524929 * 153849834
%e A218165 853910661121  with A208178(1) = 257.
%t A218165 aa = {}; Do[p = Prime[n]; If[Mod[p, 256] == 1, k = 1; While[ ! Mod[k^128 + 1, p] == 0, k++ ]; AppendTo[aa, k]], {n, 5000}]; aa
%Y A218165 Cf. A208178.
%K A218165 nonn
%O A218165 1,1
%A A218165 _Michel Lagneau_, Oct 22 2012