A272035 Numbers n such that the sum of the inverse of the exponents in the binary expansion of 2n is an integer.

0, 1, 38, 39, 2090, 2091, 16902, 16903, 18954, 18955, 18988, 18989, 131334, 131335, 133386, 133387, 133420, 133421, 148258, 148259, 150284, 150285, 524314, 524315, 524348, 524349, 526386, 526387, 541212, 541213, 543250, 543251, 543284, 543285, 655644, 655645, 657682

Offset

1,3

Comments

That is, numbers such that A116416(n) equals 1.

2k is in this sequence if and only if 2k + 1 is. Therefore n + a(n) is odd for all n. - Peter Kagey, Apr 19 2016

Links

Peter Kagey, Table of n, a(n) for n = 1..450 (All terms less than 2^30)

Example

For n=39, 39_10=100111_2, and 1/1 + 1/2 + 1/3 + 1/6 = 2, an integer.

Mathematica

Select[Range[2^20], IntegerQ@ Total[1/Flatten@ Position[Reverse@ IntegerDigits[#, 2], 1]] &] (* Michael De Vlieger, Apr 18 2016 *)

Prog

(PARI) isok(n) = {my(b = Vecrev(binary(n))); denominator(sum(k=1, #b, b[k]/k)) == 1; }

Crossrefs

Cf. A116416, A116417, A272034, A272036, A272082.

Sequence in context: A031958 A288036 A350854 * A056027 A072585 A050874

Adjacent sequences: A272032 A272033 A272034 * A272036 A272037 A272038

Keyword

nonn

Author

Michel Marcus, Apr 18 2016

Status

approved