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A121153
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Numbers n with the property that 1/n can be written in base 3 in such a way that the fractional part contains no 1's.
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12
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1, 3, 4, 9, 10, 12, 13, 27, 28, 30, 36, 39, 40, 81, 82, 84, 90, 91, 108, 117, 120, 121, 243, 244, 246, 252, 270, 273, 324, 328, 351, 360, 363, 364, 729, 730, 732, 738, 756, 757, 810, 819, 820, 949, 972, 984, 1036, 1053, 1080, 1089, 1092, 1093, 2187
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OFFSET
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1,2
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COMMENTS
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Numbers n such that 1/n is in the Cantor set.
A subsequence of A054591. The first member of A054591 which does not belong to this sequence is 146. See A135666.
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LINKS
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EXAMPLE
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1/3 in base 3 can be written as either .1 or .0222222... The latter version contains no 1's, so 3 is in the sequence.
1/4 in base 3 is .02020202020..., so 4 is in the sequence.
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MATHEMATICA
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(Mma code from T. D. Noe, Feb 20 2010. This produces the sequence except for the powers of 3.)
# Find the length of the periodic part of the fraction:
FracLen[n_] := Module[{r = n/3^IntegerExponent[n, 3]}, MultiplicativeOrder[3, r]]
# Generate the fractions and select those that have no 1's:
Select[Range[100000], ! MemberQ[Union[RealDigits[1/#, 3, FracLen[ # ]][[1]]], 1] &]
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PROG
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(PARI) is(n, R=divrem(3^logint(n, 3), n), S=0)={while(R[1]!=1&&!bittest(S, R[2]), S+=1<<R[2]; R=divrem(R[2]*3, n)); R[1]!=1||R[2]==0} \\ M. F. Hasler, Feb 27 2018
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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