A385225 Primes p such that multiplicative order of -5 modulo p is odd.

2, 3, 7, 23, 29, 43, 47, 61, 67, 83, 103, 107, 127, 163, 167, 223, 227, 229, 263, 283, 307, 347, 349, 367, 383, 421, 443, 449, 463, 467, 487, 503, 509, 521, 523, 547, 563, 587, 607, 643, 647, 661, 683, 701, 709, 727, 743, 761, 787, 821, 823, 827, 863, 883, 887, 907, 947, 967, 983

Offset: 1

Author

Jianing Song, Jun 22 2025

Keywords

• nonn
• easy

Comments

The multiplicative order of -5 modulo a(n) is A385231(n).

Contained in primes congruent to 1, 3, 7, 9 modulo 20 (primes p such that -5 is a quadratic residue modulo p, A139513), and contains primes congruent to 3, 7 modulo 20 (A122870).

Conjecture: this sequence has density 1/3 among the primes.

Links

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

Crossrefs

Subsequence of A139513. Contains A122870 as a subsequence.

Cf. A385231 (the actual multiplicative orders).

Cf. other bases: A014663 (base 2), A385220 (base 3), A385221 (base 4), A385192 (base 5), A163183 (base -2), A385223 (base -3), A385224 (base -4), this sequence (base -5).

Programs

Mathematica

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

PARI

isA385225(p) = isprime(p) && (p!=5) && znorder(Mod(-5,p))%2