A284602 Numbers k such that the decimal representation of 1/k is either finite or has even period.

1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 21, 22, 23, 25, 26, 28, 29, 32, 33, 34, 35, 38, 39, 40, 42, 44, 46, 47, 49, 50, 51, 52, 55, 56, 57, 58, 59, 61, 63, 64, 65, 66, 68, 69, 70, 73, 76, 77, 78, 80, 84, 85, 87, 88, 89, 91, 92, 94, 95, 97, 98, 99, 100, 101, 102, 103, 104, 105, 109, 110, 112, 113, 114, 115

Offset

1,2

Comments

All numbers of the form 2^i*5^j with i, j >= 0 are in this sequence (numbers with a finite decimal expansion).

From Robert G. Wilson v, Apr 02 2017: (Start)

If k is in the sequence, then so are 2k and 5k.

The complement of A284601.

Primitives: 1, 7, 11, 13, 17, 19, 21, 23, 29, 33, 39, 47, 49, 51, 57, 59, 61, 63, ..., .

(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

14 is in the sequence because 1/14 = 0.0714285(714285)..., whose period is 6, an even number.

Mathematica

Select[Range[115], Mod[Length[RealDigits[1/#][[1, -1]]], 2] == 0 & ]

Crossrefs

Cf. A002371, A003592, A028416, A051626, A206586, A284601.

Sequence in context: A189784 A062005 A039018 * A286355 A292665 A240977

Adjacent sequences: A284599 A284600 A284601 * A284603 A284604 A284605

Keyword

nonn,base

Author

Ilya Gutkovskiy, Mar 30 2017

Status

approved