A211244 Order of 8 mod n-th prime: least k such that prime(n) divides 8^k-1.

0, 2, 4, 1, 10, 4, 8, 6, 11, 28, 5, 12, 20, 14, 23, 52, 58, 20, 22, 35, 3, 13, 82, 11, 16, 100, 17, 106, 12, 28, 7, 130, 68, 46, 148, 5, 52, 54, 83, 172, 178, 60, 95, 32, 196, 33, 70, 37, 226, 76, 29, 119, 8, 50, 16, 131, 268, 45, 92, 70, 94, 292, 34, 155, 52

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

Crossrefs

Cf. A053451 (order of 8 mod 2n+1), A019338 (full reptend primes in base 8).

In other bases: A014664, A062117, A082654, A211241, A211242, A211243, A211245, A002371, A372801.

Programs

GAP

A000040:=Filtered([1..350],IsPrime);;
List([1..Length(A000040)],n->OrderMod(8,A000040[n])); # Muniru A Asiru, Feb 06 2019

Mathematica

nn = 8; Table[If[Mod[nn, p] == 0, 0, MultiplicativeOrder[nn, p]], {p, Prime[Range[100]]}]

PARI

a(n,{base=8}) = my(p=prime(n)); if(base%p, znorder(Mod(base,p)), 0) \\ Jianing Song, May 13 2024

Formula

a(n) = A014664(n)/gcd(3, A014664(n)). - Jianing Song, May 13 2024