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

%I A211242 #19 Jul 17 2024 04:47:40
%S A211242 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,
%T A211242 10,102,106,108,112,126,130,136,23,37,150,156,27,83,43,178,60,19,96,
%U A211242 14,198,105,222,226,228,232,17,20,250,256,131,134,270,276,56,141
%N A211242 Order of 6 mod n-th prime: least k such that prime(n) divides 6^k-1.
%H A211242 T. D. Noe, <a href="/A211242/b211242.txt">Table of n, a(n) for n = 1..1000</a>
%p A211242 A211242 := proc(n)
%p A211242     if n<= 2 then
%p A211242         0 ;
%p A211242     else
%p A211242         numtheory[order](6,ithprime(n)) ;
%p A211242     end if;
%p A211242 end proc:
%p A211242 seq(A211242(n),n=1..80) ; # _R. J. Mathar_, Jul 17 2024
%t A211242 nn = 6; Table[If[Mod[nn, p] == 0, 0, MultiplicativeOrder[nn, p]], {p, Prime[Range[100]]}]
%o A211242 (GAP) A000040:=Filtered([1..350],IsPrime);;
%o A211242 List([1..Length(A000040)],n->OrderMod(6,A000040[n])); # _Muniru A Asiru_, Feb 06 2019
%o A211242 (PARI) a(n,{base=6}) = my(p=prime(n)); if(base%p, znorder(Mod(base,p)), 0) \\ _Jianing Song_, May 13 2024
%Y A211242 Cf. A019336 (full reptend primes in base 6).
%Y A211242 In other bases: A014664, A062117, A082654, A211241, A211243, A211244, A211245, A002371.
%K A211242 nonn,easy
%O A211242 1,4
%A A211242 _T. D. Noe_, Apr 11 2012