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A187041 Numbers for which Midy's theorem does not hold.

%I A187041 #15 Aug 03 2014 14:01:28
%S A187041 1,2,3,4,5,6,8,9,10,12,15,16,18,20,21,24,25,27,30,31,32,33,36,37,39,
%T A187041 40,41,42,43,45,48,50,51,53,54,57,60,62,63,64,66,67,69,71,72,74,75,78,
%U A187041 79,80,81,82,83,84,86,87,90,93,96,99,100,102,105,106,107,108,111,114,117,119,120,123,124,125,126,128,129,132,134,135,138,141,142,144,147,148,150
%N A187041 Numbers for which Midy's theorem does not hold.
%H A187041 Wikipedia, <a href="http://en.wikipedia.org/wiki/Midy%27s_theorem">Midy's theorem</a>
%p A187041 fct1 := proc(an) local i,st:  st := 0:
%p A187041 for i from 1 to nops(an)/2 do
%p A187041    st := op(i,an)*10^(nops(an)/2-i) + st
%p A187041 od: RETURN(st):  end:
%p A187041 fct2 := proc(an) local i,st:  st := 0:
%p A187041 for i from nops(an)/2+1 to nops(an) do
%p A187041    st := op(i,an)*10^(nops(an)/2-i+nops(an)/2) + st
%p A187041 od:  RETURN(st):  end:
%p A187041 A187041 := proc(n) local st:
%p A187041 st := op(4,numtheory[pdexpand](1/n));
%p A187041 if (modp(nops(st),2) <> 0 or nops(st) = 1 or n = 1) then
%p A187041      RETURN(n)
%p A187041 elif (modp(nops(st),2) = 0) then
%p A187041    if not(10^(nops(st)/2)-1 - (fct1(st)+fct2(st)) = 0) then
%p A187041        RETURN(n)
%p A187041 fi: fi: end:  seq(A187041(n), n=1..250);
%t A187041 okQ[n_] := Module[{ps = First /@ FactorInteger[n], d, len}, If[n < 2 || Complement[ps, {2, 5}] == {}, False, d = RealDigits[1/n, 10][[1, -1]]; len = Length[d]; EvenQ[len] && Union[Total[Partition[d, len/2]]] == {9}]]; Select[Range[300], ! okQ[#] &] (* _T. D. Noe_, Mar 02 2011 *)
%Y A187041 Cf. A028416, A187040.
%K A187041 nonn,base
%O A187041 1,2
%A A187041 _Jani Melik_, Mar 02 2011
%E A187041 Corrected by _T. D. Noe_, Mar 02 2011