

A176351


Numbers n such that 2*3^n + 1 is a primitive prime factor of 10^3^n  1.


0




OFFSET

1,1


COMMENTS

Consider the problem of finding the smallest number k such that the decimal representation of 1/k has period 3^e for a given e. The number k is usually 3^(e+2). However, if e is one of the n in this sequence, then the prime 2*3^n+1 is a smaller k. The first instance of these exceptions is 1/163, which has a period of 81.
10 must be a square residue modulo 2*3^n + 1, implying that n must be a multiple of 4.


LINKS



MATHEMATICA

Select[Range[10000], PrimeQ[1+2*3^# ] && MultiplicativeOrder[10, 1+2*3^# ] == 3^# &]


CROSSREFS

Cf. A003306 (primes of the form 2*3^n+1), A003060 (least k such that 1/k has period n).


KEYWORD

hard,more,nonn


AUTHOR



EXTENSIONS



STATUS

approved



