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%I #18 Oct 10 2019 10:20:20
%S 3,17,73,101,137,163,257,353,449,577,641,751,757,883,1297,1409,1801,
%T 3137,3529,5477,7057,7351,8929,9397,10753,11831,12101,13457,13553,
%U 14401,15361,15377,15973,18523,19841,20809,21401,21601,23549,24001,24337
%N Primes p for which the period length of 1/p is a perfect power, A001597.
%C 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,....
%C The primes modulo any integer do not seem to be equally distributed.
%H Ray Chandler & Robert G. Wilson v, <a href="/A128948/b128948.txt">Table of n, a(n) for n = 1..30000</a>
%H <a href="/index/1#1overn">Index entries for sequences related to decimal expansion of 1/n</a>
%e The prime 73 has a period of 8 = 2^3 which is a member of A001597, hence is a member of this sequence.
%t 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 *)
%Y Cf. A001597, A072859, A072982.
%K base,nonn
%O 1,1
%A _Robert G. Wilson v_, May 05 2007
%E Correction (3 is a member of the sequence) from Ray Chandler, May 11 2007
%E B-file corrected by _Ray Chandler_, Oct 23 2011