A284602 - OEIS

%I #29 Nov 19 2023 21:17:11

%S 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,

%T 38,39,40,42,44,46,47,49,50,51,52,55,56,57,58,59,61,63,64,65,66,68,69,

%U 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

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

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

%C From _Robert G. Wilson v_, Apr 02 2017: (Start)

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

%C The complement of A284601.

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

%C (End)

%H Robert G. Wilson v, <a href="/A284602/b284602.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/1#1overn">Index entries for sequences related to decimal expansion of 1/n</a>

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

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

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

%K nonn,base

%O 1,2

%A _Ilya Gutkovskiy_, Mar 30 2017