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%I #16 Aug 26 2021 20:16:57
%S 11,13,157,5,22621,7,659,89,37,19141,23,20593,477517,211,61,17,
%T 2693651,1657,29043636306420266077,85403261,8177824843189,57154490053,
%U 47,193,303551,79,306829,673,59,31,373,153953,886381,2551,71,73,3933841,3307
%N Smallest primitive prime factor of 12^n-1.
%C Also, smallest prime p such that 1/p has duodecimal period n.
%H Max Alekseyev, <a href="/A252170/b252170.txt">Table of n, a(n) for n = 1..310</a>
%e a(4) = 5 because 1/5 = 0.249724972497... and 5 is the smallest prime with period 4 in base 12.
%e a(5) = 22621 because 1/22621 = 0.0000100001... and 22621 is the smallest (in fact, the only one) prime with period 5 in base 12.
%p S:= {}:
%p for n from 1 to 72 do
%p F:= numtheory:-factorset(12^n-1) minus S;
%p A[n]:= min(F);
%p S:= S union F;
%p od:
%p seq(A[n], n=1..72);
%t prms={}; Table[f=First/@FactorInteger[12^n-1]; p=Complement[f, prms]; prms=Join[prms, p]; If[p=={}, 1, First[p]], {n, 72}]
%o (PARI) listap(nn) = {prf = []; for (n=1, nn, vp = (factor(12^n-1)[,1])~; f = setminus(Set(vp), Set(prf)); prf = concat(prf, f); print1(vecmin(Vec(f)), ", "););} \\ _Michel Marcus_, Dec 15 2014; after A007138
%Y Cf. A007138 (decimal version).
%Y Cf. A246004, A246489.
%K nonn
%O 1,1
%A _Eric Chen_, Dec 15 2014
%E Edited by _Max Alekseyev_, Aug 26 2021
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