cp's OEIS Frontend

A186640 Primes p such that the decimal expansion of 1/p has a periodic part of even length, but are not cyclic numbers (A001913).

%I A186640 #15 Oct 01 2012 15:37:32
%S A186640 11,13,73,89,101,103,127,137,139,157,197,211,241,251,281,293,331,349,
%T A186640 353,373,401,409,421,449,457,463,521,557,569,601,607,617,641,653,661,
%U A186640 673,677,691,739,761,769,809,829,859,877,881,929,967,997,1009,1049,1061
%N A186640 Primes p such that the decimal expansion of 1/p has a periodic part of even length, but are not cyclic numbers (A001913).
%H A186640 T. D. Noe, <a href="/A186640/b186640.txt">Table of n, a(n) for n = 1..1000</a>
%F A186640 p in A028416, but not A001913.
%p A186640 f1_d := proc(n) local st, period:
%p A186640 st := ithprime(n):
%p A186640 period := numtheory[order](10,st):
%p A186640 if (modp(period,2) = 0) then
%p A186640    if (st-1 <> period) then
%p A186640       RETURN(st):
%p A186640    fi:
%p A186640 fi: end:  seq(f1_d(n), n=1..200);
%t A186640 Select[Prime[Range[200]], EvenQ[Length[RealDigits[1/#][[1, 1]]]] && MultiplicativeOrder[10, #] != # - 1 &] (* _T. D. Noe_, Oct 01 2012 *)
%o A186640 (PARI) is(p)=if(p>9 && isprime(p), my(o=znorder(Mod(10, p))); o%2==0 && o+1!=p, 0) \\ _Charles R Greathouse IV_, Oct 01 2012
%Y A186640 Cf. A028416.
%K A186640 nonn,base
%O A186640 1,1
%A A186640 _Jani Melik_, Feb 24 2011