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A284601 Numbers k such that the decimal representation of 1/k does not terminate and has odd period. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
From Robert G. Wilson v, Apr 02 2017: (Start)
If k is in the sequence, then so are 2k and 5k.
The complement of A284602.
Primitives: 3, 9, 27, 31, 37, 41, 43, 53, 67, 71, 79, 81, 83, 93, 107, 111, 123, ..., .
(End)
From Robert Israel, Apr 03 2017: (Start)
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)
LINKS
EXAMPLE
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.
MAPLE
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:
select(filter, [$1..1000]); # Robert Israel, Apr 03 2017
MATHEMATICA
Select[Range[215], Mod[Length[RealDigits[1/#][[1, -1]]], 2] == 1 & ]
CROSSREFS
Sequence in context: A028251 A194226 A193803 * A039004 A070021 A083354
KEYWORD
nonn,base
AUTHOR
Ilya Gutkovskiy, Mar 30 2017
STATUS
approved

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Last modified March 29 06:44 EDT 2024. Contains 371265 sequences. (Running on oeis4.)