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A284601
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Numbers k such that the decimal representation of 1/k does not terminate and has odd period.
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3
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3, 6, 9, 12, 15, 18, 24, 27, 30, 31, 36, 37, 41, 43, 45, 48, 53, 54, 60, 62, 67, 71, 72, 74, 75, 79, 81, 82, 83, 86, 90, 93, 96, 106, 107, 108, 111, 120, 123, 124, 129, 134, 135, 142, 144, 148, 150, 151, 155, 158, 159, 162, 163, 164, 166, 172, 173, 180, 185, 186, 191, 192, 199, 201, 205, 212, 213, 214, 215
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OFFSET
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1,1
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COMMENTS
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If k is in the sequence, then so are 2k and 5k.
Primitives: 3, 9, 27, 31, 37, 41, 43, 53, 67, 71, 79, 81, 83, 93, 107, 111, 123, ..., .
(End)
Numbers of the form 2^j * 5^k * m where m > 1, gcd(m,10)=1 and the multiplicative order of 10 (mod m) is odd.
Complement of A003592 in the multiplicative semigroup generated by A186635, i.e., numbers whose prime factors are in A186635 with at least one prime factor not 2 or 5. (End)
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LINKS
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EXAMPLE
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27 is in the sequence because 1/27 = 0.0370(370)... period is 3, 3 is odd.
2 and 5 are not in the sequence because 1/2 = 0.5 and 1/5 = 0.2 are terminating expansions. See also comments in A051626 and A284602.
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MAPLE
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filter:= proc(n) local m;
m:= n/2^padic:-ordp(n, 2);
m:= m/5^padic:-ordp(m, 5);
m > 1 and numtheory:-order(10, m)::odd
end proc:
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MATHEMATICA
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Select[Range[215], Mod[Length[RealDigits[1/#][[1, -1]]], 2] == 1 & ]
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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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STATUS
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approved
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