A218162 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)).

19, 8, 15, 6, 10, 33, 4, 107, 43, 170, 194, 21, 86, 10, 109, 6, 31, 227, 212, 108, 75, 5, 13, 21, 36, 516, 119, 68, 69, 264, 281, 634, 186, 214, 210, 50, 397, 277, 227, 112, 461, 329, 47, 1399, 257, 231, 131, 68, 530, 981, 242, 298, 219, 508, 196, 266, 97, 234

Offset

1,1

Comments

A133870(n) : primes of form 32n+1.

Links

Table of n, a(n) for n=1..58.

Example

a(5) = 10 because 10^16+1 = 10000000000000001 = 353 * 449 * 641 * 1409 * 69857 with A133870(5) = 449.

Mathematica

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

Crossrefs

Cf. A133870.

Sequence in context: A040346 A364786 A124608 * A064264 A040345 A070685

Adjacent sequences: A218159 A218160 A218161 * A218163 A218164 A218165

Keyword

nonn

Author

Michel Lagneau, Oct 22 2012

Status

approved