A053448 Multiplicative order of 5 mod m, where gcd(m, 5) = 1.

1, 1, 2, 1, 2, 6, 2, 6, 5, 2, 4, 6, 4, 16, 6, 9, 6, 5, 22, 2, 4, 18, 6, 14, 3, 8, 10, 16, 6, 36, 9, 4, 20, 6, 42, 5, 22, 46, 4, 42, 16, 4, 52, 18, 6, 18, 14, 29, 30, 3, 6, 16, 10, 22, 16, 22, 5, 6, 72, 36, 9, 30, 4, 39, 54, 20, 82, 6, 42, 14, 10, 44, 12, 22, 6, 46, 8, 96, 42, 30, 25, 16

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Essentially the same as A050977. - R. J. Mathar, Oct 21 2012

Crossrefs

Cf. A047201, A002326 (order of 2), A053446 (order of 3), A053447 (order of 4).

Programs

Mathematica

MultiplicativeOrder[5, #] & /@ Select[ Range@ 100, GCD[5, #] == 1 &] (* Robert G. Wilson v, Apr 05 2011 *)

PARI

lista(nn) = {for(n=1, nn, if (gcd(n, 5) == 1, print1(znorder(Mod(5, n)), ", ")););} \\ Michel Marcus, Feb 09 2015

Formula

a(n) = multiplicative order of 5 modulo floor((5*n-1)/4), for n >= 1. This modulus is A047201(n). - Wolfdieter Lang, Sep 30 2020