A211241 Order of 5 mod n-th prime: least k such that prime(n) divides 5^k-1.

1, 2, 0, 6, 5, 4, 16, 9, 22, 14, 3, 36, 20, 42, 46, 52, 29, 30, 22, 5, 72, 39, 82, 44, 96, 25, 102, 106, 27, 112, 42, 65, 136, 69, 37, 75, 156, 54, 166, 172, 89, 15, 19, 192, 196, 33, 35, 222, 226, 114, 232, 119, 40, 25, 256, 262, 67, 27, 276, 140, 282, 292

Offset: 1

Author

T. D. Noe, Apr 11 2012

Keywords

• nonn
• easy

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• Alexandre Zalesski, Unisingular subgroups of symplectic group Sp_2n(2) for 2n < 250, arXiv:2401.16075 [math.GR], 2024. See p. 52.

Crossrefs

Cf. A019335 (full reptend primes in base 5).

In other bases: A014664, A062117, A082654, A211242, A211243, A211244, A211245, A002371.

Programs

GAP

A000040:=Filtered([1..350],IsPrime);;
List([1..Length(A000040)],n->OrderMod(5,A000040[n])); # Muniru A Asiru, Feb 06 2019

Mathematica

nn = 5; Table[If[Mod[nn, p] == 0, 0, MultiplicativeOrder[nn, p]], {p, Prime[Range[100]]}]

PARI

a(n,{base=5}) = my(p=prime(n)); if(base%p, znorder(Mod(base,p)), 0) \\ Jianing Song, May 13 2024