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A187041 Numbers for which Midy's theorem does not hold. 2
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, 40, 41, 42, 43, 45, 48, 50, 51, 53, 54, 57, 60, 62, 63, 64, 66, 67, 69, 71, 72, 74, 75, 78, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..87.

Wikipedia, Midy's theorem

MAPLE

fct1 := proc(an) local i, st:  st := 0:

for i from 1 to nops(an)/2 do

   st := op(i, an)*10^(nops(an)/2-i) + st

od: RETURN(st):  end:

fct2 := proc(an) local i, st:  st := 0:

for i from nops(an)/2+1 to nops(an) do

   st := op(i, an)*10^(nops(an)/2-i+nops(an)/2) + st

od:  RETURN(st):  end:

A187041 := proc(n) local st:

st := op(4, numtheory[pdexpand](1/n));

if (modp(nops(st), 2) <> 0 or nops(st) = 1 or n = 1) then

     RETURN(n)

elif (modp(nops(st), 2) = 0) then

   if not(10^(nops(st)/2)-1 - (fct1(st)+fct2(st)) = 0) then

       RETURN(n)

fi: fi: end:  seq(A187041(n), n=1..250);

MATHEMATICA

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 *)

CROSSREFS

Cf. A028416, A187040.

Sequence in context: A243355 A233461 A010432 * A097752 A014866 A051661

Adjacent sequences:  A187038 A187039 A187040 * A187042 A187043 A187044

KEYWORD

nonn,base

AUTHOR

Jani Melik, Mar 02 2011

EXTENSIONS

Corrected by T. D. Noe, Mar 02 2011

STATUS

approved

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Last modified May 7 16:00 EDT 2021. Contains 343652 sequences. (Running on oeis4.)