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

1,1

Comments

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

Links

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

Example

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.

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}]

Prog

(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

Crossrefs

Cf. A007138 (decimal version).

Cf. A246004, A246489.

Sequence in context: A136296 A094621 A178426 * A366718 A144375 A140969

Adjacent sequences: A252167 A252168 A252169 * A252171 A252172 A252173

Keyword

nonn

Author

Eric Chen, Dec 15 2014

Extensions

Edited by Max Alekseyev, Aug 26 2021

Status

approved