A385227 Odd multiplicative orders of 4 modulo primes.

1, 3, 5, 9, 11, 5, 7, 23, 29, 33, 35, 9, 39, 41, 11, 51, 53, 7, 65, 69, 15, 81, 83, 89, 95, 99, 105, 37, 113, 29, 119, 25, 131, 135, 35, 47, 51, 155, 15, 21, 173, 179, 183, 189, 191, 209, 43, 73, 221, 231, 233, 239, 243, 245, 83, 251, 261, 273, 281, 57, 293

Offset: 1

Author

Jianing Song, Jun 22 2025

Keywords

• nonn
• easy

Comments

a(n) is the multiplicative order of 4 modulo A385221(n).

Odd elements in A082654.

Links

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

Crossrefs

Cf. A082654, A385221 (corresponding primes).

Cf. other bases: A139686 (base 2), A385226 (base 3), this sequence (base 4), A385193 (base 5), A385228 (base -2), A385229 (base -3), A385230 (base -4), A385231 (base -5).

Programs

Mathematica

Select[Map[MultiplicativeOrder[4, #] &, Prime[Range[200]]], OddQ] (* Paolo Xausa, Jun 28 2025 *)

PARI

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