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%I #17 Mar 13 2023 07:29:59
%S 2,3,5,31,37,41,43,53,67,71,79,83,107,151,163,173,191,199,227,239,271,
%T 277,283,307,311,317,347,359,397,431,439,443,467,479,523,547,563,587,
%U 599,613,631,643,683,719,733,751,757,773,787,797,827,839,853,883,907,911,919,947,991,1013,1031,1039,1093,1123,1151,1163,1187
%N Primes p such that the decimal expansion of 1/p has a periodic part of odd length.
%C Interestingly, the initial terms of A040119 (Primes p such that x^4 = 10 has a solution mod p) are identical to the initial terms of this sequence except for 241 which is a term of A040119 but not of A186635. [_John W. Layman_, Feb 25 2011]
%C There are many numbers in A040119 that are not here: 241, 641, 769, 809, 1009, 1409, 1601, 1721.... - _T. D. Noe_, Feb 25 2011
%p Ax := proc(n) local st:
%p st := ithprime(n):
%p if (modp(numtheory[order](10,st),2) <> 0) then
%p RETURN(st)
%p fi: end: seq(Ax(n), n=1..200);
%t Union[{2, 5}, Select[Prime[Range[200]], OddQ[Length[RealDigits[1/#][[1, 1]]]] &]]
%Y Cf. A002371, A048595, A028416, A040119.
%K nonn,base
%O 1,1
%A _Jani Melik_, Feb 24 2011
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