A211245 Order of 9 mod n-th prime: least k such that prime(n) divides 9^k-1.

1, 0, 2, 3, 5, 3, 8, 9, 11, 14, 15, 9, 4, 21, 23, 26, 29, 5, 11, 35, 6, 39, 41, 44, 24, 50, 17, 53, 27, 56, 63, 65, 68, 69, 74, 25, 39, 81, 83, 86, 89, 45, 95, 8, 98, 99, 105, 111, 113, 57, 116, 119, 60, 125, 128, 131, 134, 15, 69, 140, 141, 146, 17, 155, 39

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. A364867.

In other bases: A014664, A062117, A082654, A211241, A211242, A211243, A211244, A002371, A372801.

Programs

GAP

A000040:=Filtered([1..350],IsPrime);;
List([1..Length(A000040)],n->OrderMod(9,A000040[n])); # Muniru A Asiru, Feb 06 2019

Mathematica

nn = 9; Table[If[Mod[nn, p] == 0, 0, MultiplicativeOrder[nn, p]], {p, Prime[Range[100]]}]

PARI

a(n,{base=9}) = my(p=prime(n)); if(base%p, znorder(Mod(base,p)), 0) \\ Jianing Song, May 13 2024

Formula

From Jianing Song, May 13 2024: (Start)

a(n) = A062117(n)/gcd(2, A062117(n)).

a(n) <= (prime(n) - 1)/2. Those prime(n) for which a(n) = (prime(n) - 1)/2 are listed in A364867. (End)