A252170 Smallest primitive prime factor of 12^n-1.

11, 13, 157, 5, 22621, 7, 659, 89, 37, 19141, 23, 20593, 477517, 211, 61, 17, 2693651, 1657, 29043636306420266077, 85403261, 8177824843189, 57154490053, 47, 193, 303551, 79, 306829, 673, 59, 31, 373, 153953, 886381, 2551, 71, 73, 3933841, 3307

Offset: 1

Author

Eric Chen, Dec 15 2014

Keywords

• nonn

Comments

Also, smallest prime p such that 1/p has duodecimal period n.

Examples

			a(4) = 5 because 1/5 = 0.249724972497... and 5 is the smallest prime with period 4 in base 12.
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.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 1..310

Crossrefs

Cf. A112927 (base 2), A143663 (base 3), A112092 (base 4), A143665 (base 5), A379639 (base 6), A379640 (base 7), A379641 (base 8), A379642 (base 9), A007138 (base 10), A379644 (base 11), A252170 (base 12).

Cf. A246004, A246489.

Programs

Maple

S:= {}:
for n from 1 to 72 do
  F:= numtheory:-factorset(12^n-1) minus S;
  A[n]:= min(F);
  S:= S union F;
od:
seq(A[n], n=1..72);

Mathematica

prms={}; Table[f=First/@FactorInteger[12^n-1]; p=Complement[f, prms]; prms=Join[prms, p]; If[p=={}, 1, First[p]], {n, 72}]

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

Extensions

Edited by Max Alekseyev, Aug 26 2021