A186640 - OEIS

%I #15 Oct 01 2012 15:37:32

%S 11,13,73,89,101,103,127,137,139,157,197,211,241,251,281,293,331,349,

%T 353,373,401,409,421,449,457,463,521,557,569,601,607,617,641,653,661,

%U 673,677,691,739,761,769,809,829,859,877,881,929,967,997,1009,1049,1061

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

%H T. D. Noe, <a href="/A186640/b186640.txt">Table of n, a(n) for n = 1..1000</a>

%F p in A028416, but not A001913.

%p f1_d := proc(n) local st, period:

%p st := ithprime(n):

%p period := numtheory[order](10,st):

%p if (modp(period,2) = 0) then

%p    if (st-1 <> period) then

%p       RETURN(st):

%p    fi:

%p fi: end:  seq(f1_d(n), n=1..200);

%t Select[Prime[Range[200]], EvenQ[Length[RealDigits[1/#][[1, 1]]]] && MultiplicativeOrder[10, #] != # - 1 &] (* _T. D. Noe_, Oct 01 2012 *)

%o (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 Cf. A028416.

%K nonn,base

%O 1,1

%A _Jani Melik_, Feb 24 2011