A385230 Odd multiplicative orders of -4 modulo primes.

1, 3, 7, 9, 5, 13, 15, 25, 9, 7, 17, 37, 13, 43, 45, 49, 19, 67, 23, 73, 39, 79, 87, 93, 97, 11, 51, 105, 19, 115, 127, 65, 135, 139, 71, 37, 153, 163, 165, 169, 175, 177, 61, 189, 95, 193, 199, 101, 205, 207, 213, 107, 219, 235, 17, 83, 23, 85, 265, 89, 91, 277, 279, 141, 59, 75

Offset: 1

Author

Jianing Song, Jun 22 2025

Keywords

• nonn
• easy

Comments

Odd elements in A380531.

a(n) is the multiplicative order of -4 modulo A385224(n).

Links

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

Crossrefs

Cf. A380531, A385224 (corresponding primes).

Cf. other bases: A139686 (base 2), A385226 (base 3), A385227 (base 4), A385193 (base 5), A385228 (base -2), A385229 (base -3), this sequence (base -4), A385231 (base -5).

Programs

Mathematica

Select[Map[MultiplicativeOrder[-4, #] &, Prime[Range[200]]], OddQ] (* Paolo Xausa, Jun 30 2025 *)

PARI

forprime(p=3, 1e4, z=znorder(Mod(-4, p)); if(z%2, print1(z, ", ")))