A385229 Odd multiplicative orders of -3 modulo primes.

1, 3, 9, 15, 9, 21, 5, 11, 39, 17, 63, 69, 25, 39, 81, 99, 105, 111, 15, 141, 17, 165, 87, 61, 93, 189, 99, 73, 231, 243, 83, 29, 7, 285, 303, 51, 103, 315, 107, 11, 345, 121, 369, 375, 131, 405, 411, 71, 429, 219, 63, 453, 153, 117, 161, 165, 83, 17, 519, 105, 531, 267, 543, 561, 117

Offset: 1

Author

Jianing Song, Jun 22 2025

Keywords

• nonn
• easy

Comments

Odd elements in A380482.

a(n) is the multiplicative order of -3 modulo A385223(n).

Links

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

Crossrefs

Cf. A380482, A385223 (corresponding primes).

Cf. other bases: A139686 (base 2), A385226 (base 3), A385227 (base 4), A385193 (base 5), A385228 (base -2), this sequence (base -3), A385230 (base -4), A385231 (base -5).

Programs

Mathematica

Select[Map[MultiplicativeOrder[-3, #] &, Prime[Range[200]]], OddQ] (* Paolo Xausa, Jun 30 2025 *)

PARI

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