A218154 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).

3, 8, 35, 3, 44, 2, 30, 36, 30, 151, 35, 27, 82, 16, 8, 27, 68, 40, 52, 62, 67, 104, 287, 98, 157, 63, 100, 143, 99, 257, 36, 189, 151, 458, 108, 155, 348, 105, 227, 598, 67, 25, 460, 169, 250, 342, 24, 423, 286, 221, 627, 113, 107, 206, 279, 506, 630, 57, 39

Offset: 1

Author

Michel Lagneau, Oct 22 2012

Keywords

• nonn

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Maple

P:= select(isprime, [seq(i,i=1..10000,16)]):
map(t -> min(map(rhs@op, [msolve(k^8+1=0,t)])), P); # Robert Israel, May 15 2019

Mathematica

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