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

1,1

Links

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

Example

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

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

Crossrefs

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

Sequence in context: A063805 A125046 A270378 * A349968 A204451 A077291

Adjacent sequences: A218151 A218152 A218153 * A218155 A218156 A218157

Keyword

nonn

Author

Michel Lagneau, Oct 22 2012

Status

approved