A385193 Odd multiplicative orders of 5 modulo primes.

1, 5, 9, 3, 29, 5, 39, 25, 27, 65, 69, 37, 75, 89, 15, 19, 33, 35, 119, 25, 67, 27, 155, 165, 179, 21, 97, 25, 17, 209, 215, 219, 115, 239, 245, 249, 135, 71, 285, 299, 309, 35, 329, 115, 359, 123, 375, 405, 9, 419, 429, 455, 459, 235, 485, 495, 509, 255, 515, 173, 525, 265, 267, 109, 575, 45

Offset: 1

Author

Jianing Song, Jun 20 2025

Keywords

• nonn
• easy

Comments

a(n) is the multiplicative order of 5 modulo A385192(n).

Odd elements in A211241.

Examples

			a(8) = 25 since it is the multiplicative order of 5 modulo A385192(8) = 101, and it is odd.
		

Links

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

Crossrefs

Cf. A211241, A385192 (corresponding primes).

Cf. other bases: A139686 (base 2), A385226 (base 3), A385227 (base 4), this sequence (base 5), A385228 (base -2), A385229 (base -3), A385230 (base -4), A385231 (base -5).

Programs

Mathematica

Select[Map[MultiplicativeOrder[5, #] &, Prime[Range[200]]], OddQ] (* Paolo Xausa, Jun 28 2025 *)

PARI

forprime(p=2, 1e4, if(p!=5, z=znorder(Mod(5, p)); if(z%2, print1(z, ", "))))