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a(n) is the smallest positive integer k such that k^8 + 1 == 0 mod p, where p is the n-th prime of the form 1 + 16*b (see A094407).
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%I #10 May 15 2019 19:28:26

%S 3,8,35,3,44,2,30,36,30,151,35,27,82,16,8,27,68,40,52,62,67,104,287,

%T 98,157,63,100,143,99,257,36,189,151,458,108,155,348,105,227,598,67,

%U 25,460,169,250,342,24,423,286,221,627,113,107,206,279,506,630,57,39

%N a(n) is the smallest positive integer k such that k^8 + 1 == 0 mod p, where p is the n-th prime of the form 1 + 16*b (see A094407).

%H Robert Israel, <a href="/A218154/b218154.txt">Table of n, a(n) for n = 1..10000</a>

%e a(5) = 44 because 44^8+1 = 14048223625217 = 17 * 241 * 3457 * 991873 with A094407 (5) = 241.

%p P:= select(isprime, [seq(i,i=1..10000,16)]):

%p map(t -> min(map(rhs@op, [msolve(k^8+1=0,t)])), P); # _Robert Israel_, May 15 2019

%t aa = {}; Do[p = Prime[n]; If[Mod[p, 16] == 1, k = 1; While[ ! Mod[k^8 + 1, p] == 0, k++ ]; AppendTo[aa, k]], {n, 300}]; aa

%Y Cf. A094407 (primes of form 16k+1).

%K nonn

%O 1,1

%A _Michel Lagneau_, Oct 22 2012