A128948 Primes p for which the period length of 1/p is a perfect power, A001597.

3, 17, 73, 101, 137, 163, 257, 353, 449, 577, 641, 751, 757, 883, 1297, 1409, 1801, 3137, 3529, 5477, 7057, 7351, 8929, 9397, 10753, 11831, 12101, 13457, 13553, 14401, 15361, 15377, 15973, 18523, 19841, 20809, 21401, 21601, 23549, 24001, 24337

Offset: 1

Author

Robert G. Wilson v, May 05 2007

Keywords

• base
• nonn

Comments

Number of primes p < 10^n whose period length of 1/p is a perfect power: 1,3,14,24,78,173,461,1190,3235,8933,....

The primes modulo any integer do not seem to be equally distributed.

Examples

			The prime 73 has a period of 8 = 2^3 which is a member of A001597, hence is a member of this sequence.
		

Links

• Ray Chandler & Robert G. Wilson v, Table of n, a(n) for n = 1..30000
• Index entries for sequences related to decimal expansion of 1/n

Crossrefs

Cf. A001597, A072859, A072982.

Programs

Mathematica

lst = {3}; p = 1; While[p < 10^8, p = NextPrime@p; If[GCD @@ Last /@ FactorInteger@ MultiplicativeOrder[10, p] > 1, AppendTo[lst, p]; Print@p]]; lst (* Ray Chandler, May 11 2007 *)

Extensions

Correction (3 is a member of the sequence) from Ray Chandler, May 11 2007

B-file corrected by Ray Chandler, Oct 23 2011