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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
OFFSET
1,2
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
Sequence in context: A243355 A233461 A010432 * A364560 A097752 A014866
KEYWORD
nonn,base
AUTHOR
Jani Melik, Mar 02 2011
EXTENSIONS
Corrected by T. D. Noe, Mar 02 2011
STATUS
approved