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

Author

Ilya Gutkovskiy, Mar 30 2017

Keywords

• nonn
• base

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)

Examples

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

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

Crossrefs

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

Programs

Mathematica

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