%I #22 May 13 2024 09:16:15

%S 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,

%T 102,106,27,112,42,65,136,69,37,75,156,54,166,172,89,15,19,192,196,33,

%U 35,222,226,114,232,119,40,25,256,262,67,27,276,140,282,292

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

%H T. D. Noe, <a href="/A211241/b211241.txt">Table of n, a(n) for n = 1..1000</a>

%H Alexandre Zalesski, <a href="https://arxiv.org/abs/2401.16075">Unisingular subgroups of symplectic group Sp_2n(2) for 2n < 250</a>, arXiv:2401.16075 [math.GR], 2024. See p. 52.

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

%o (GAP) A000040:=Filtered([1..350],IsPrime);;

%o List([1..Length(A000040)],n->OrderMod(5,A000040[n])); # _Muniru A Asiru_, Feb 06 2019

%o (PARI) a(n,{base=5}) = my(p=prime(n)); if(base%p, znorder(Mod(base,p)), 0) \\ _Jianing Song_, May 13 2024

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

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

%K nonn,easy

%O 1,2

%A _T. D. Noe_, Apr 11 2012