A385226 Odd multiplicative orders of 3 modulo primes.

1, 5, 3, 11, 23, 29, 35, 41, 53, 27, 65, 83, 89, 45, 95, 113, 57, 119, 125, 131, 69, 155, 39, 173, 179, 191, 209, 105, 43, 27, 221, 233, 239, 49, 251, 135, 281, 293, 299, 75, 323, 329, 31, 177, 359, 183, 371, 9, 413, 207, 419, 431, 443, 455, 473, 485, 491

Offset: 1

Author

Jianing Song, Jun 22 2025

Keywords

• nonn
• easy

Comments

a(n) is the multiplicative order of 3 modulo A385220(n).

Odd elements in A062117.

Links

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

Crossrefs

Cf. A062117, A385220 (corresponding primes).

Cf. other bases: A139686 (base 2), this sequence (base 3), A385227 (base 4), A385193 (base 5), A385228 (base -2), A385229 (base -3), A385230 (base -4), A385231 (base -5).

Programs

Mathematica

Select[Map[MultiplicativeOrder[3, #] &, Prime[Range[200]]], OddQ] (* Paolo Xausa, Jun 28 2025 *)

PARI

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