A211242 Order of 6 mod n-th prime: least k such that prime(n) divides 6^k-1.

0, 0, 1, 2, 10, 12, 16, 9, 11, 14, 6, 4, 40, 3, 23, 26, 58, 60, 33, 35, 36, 78, 82, 88, 12, 10, 102, 106, 108, 112, 126, 130, 136, 23, 37, 150, 156, 27, 83, 43, 178, 60, 19, 96, 14, 198, 105, 222, 226, 228, 232, 17, 20, 250, 256, 131, 134, 270, 276, 56, 141

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. A019336 (full reptend primes in base 6).

In other bases: A014664, A062117, A082654, A211241, A211243, A211244, A211245, A002371.

Programs

GAP

A000040:=Filtered([1..350],IsPrime);;
List([1..Length(A000040)],n->OrderMod(6,A000040[n])); # Muniru A Asiru, Feb 06 2019

Maple

A211242 := proc(n)
    if n<= 2 then
        0 ;
    else
        numtheory[order](6,ithprime(n)) ;
    end if;
end proc:
seq(A211242(n),n=1..80) ; # R. J. Mathar, Jul 17 2024

Mathematica

nn = 6; Table[If[Mod[nn, p] == 0, 0, MultiplicativeOrder[nn, p]], {p, Prime[Range[100]]}]

PARI

a(n,{base=6}) = my(p=prime(n)); if(base%p, znorder(Mod(base,p)), 0) \\ Jianing Song, May 13 2024