A380532 a(n) is the multiplicative order of -5 modulo prime(n); a(3) = 0 for completion.

1, 1, 0, 3, 10, 4, 16, 18, 11, 7, 6, 36, 20, 21, 23, 52, 58, 15, 11, 10, 72, 78, 41, 44, 96, 50, 51, 53, 54, 112, 21, 130, 136, 138, 74, 150, 156, 27, 83, 172, 178, 30, 38, 192, 196, 66, 70, 111, 113, 57, 232, 238, 40, 50, 256, 131, 134, 54, 276, 140

Offset: 1

Author

Jianing Song, Jun 27 2025

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A105877 (primes having primitive root -5).

Cf. bases 2..10: A014664, A062117, A082654, A211241, A211242, A211243, A211244, A211245, A002371.

Cf. bases -2..-10: A337878 (if first term 1), A380482, A380531, this sequence, A380533, A380540, A380541, A380542, A385222.

Programs

Mathematica

A380532[n_] := If[n == 3, 0, MultiplicativeOrder[-5, Prime[n]]];
Array[A380532, 100] (* Paolo Xausa, Jun 29 2025 *)

PARI

a(n,{k=-5}) = my(p = prime(n)); if(k%p==0, 0, znorder(Mod(k,p)))