A385228 Odd multiplicative orders of -2 modulo primes.

1, 5, 9, 7, 29, 33, 41, 53, 65, 69, 81, 89, 105, 113, 25, 35, 47, 51, 15, 173, 189, 209, 221, 233, 245, 83, 261, 273, 281, 57, 293, 77, 309, 107, 329, 11, 115, 123, 393, 135, 413, 429, 441, 453, 473, 97, 509, 129, 131, 175, 545, 137, 561, 83, 585, 593, 149, 629, 641, 645, 653, 713, 725

Offset

1,2

Comments

a(n) is the multiplicative order of -2 modulo A163183(n).

Odd elements in A337878 (with first term changed to 1).

Links

Jianing Song, Table of n, a(n) for n = 1..10000

Mathematica

Select[Map[MultiplicativeOrder[-2, #] &, Prime[Range[250]]], OddQ] (* Paolo Xausa, Jun 28 2025 *)

Prog

(PARI) forprime(p=3, 1e4, z=znorder(Mod(-2, p)); if(z%2, print1(z, ", ")))

Crossrefs

Cf. A337878, A163183 (corresponding primes).

Cf. other bases: A139686 (base 2), A385226 (base 3), A385227 (base 4), A385193 (base 5), this sequence (base -2), A385229 (base -3), A385230 (base -4), A385231 (base -5).

Sequence in context: A055566 A255247 A366841 * A395469 A153610 A395806

Adjacent sequences: A385225 A385226 A385227 * A385229 A385230 A385231

Keyword

nonn,easy

Author

Jianing Song, Jun 22 2025

Status

approved