|
|
A252170
|
|
Smallest primitive prime factor of 12^n-1.
|
|
3
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Also, smallest prime p such that 1/p has duodecimal period n.
|
|
LINKS
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|