A284601 Numbers k such that the decimal representation of 1/k does not terminate and has odd period.

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

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

Robert G. Wilson v, Table of n, a(n) for n = 1..10000

Index entries for sequences related to decimal expansion of 1/n

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

Cf. A002371, A003592, A003814, A051626, A186635, A284602.

Sequence in context: A028251 A194226 A193803 * A039004 A070021 A083354

Adjacent sequences: A284598 A284599 A284600 * A284602 A284603 A284604

Keyword

nonn,base

Author

Ilya Gutkovskiy, Mar 30 2017

Status

approved