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. 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.

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