A272036 Numbers n such that the sum of the inverse of the exponents in the binary expansion of 2n is equal to 1.

1, 38, 2090, 16902, 18954, 18988, 131334, 133386, 133420, 148258, 150284, 524314, 524348, 526386, 541212, 543250, 543284, 655644, 657682, 657716, 672568, 674580, 8388742, 8390794, 8390828, 8405666, 8407692, 8520098, 8522124, 8536962, 8536996, 8539048, 8913052, 8915090

Offset

1,2

Comments

That is, numbers such that both A116416(n) and A116417(n) are equal to 1.

Intersection of A272034 and A272035.

A number m with an exponent k in the binary sum must have another power of 2 having an exponent at least A275288(k). - David A. Corneth, Apr 01 2017

Links

Robert Israel, Table of n, a(n) for n = 1..1655 (first 200 terms from Peter Kagey)

Example

For n=38, 2*38_10 = 2^6 + 2^3 + 2^2 = 1001100_2, and 1/2 + 1/3 + 1/6 = 1.

Mathematica

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

Prog

(PARI) is(n) = my(b = Vecrev(binary(n))); sum(k=1, #b, b[k]/k) == 1;

Crossrefs

Cf. A116416, A116417, A272034, A272035, A272083, A275288.

Sequence in context: A221385 A158766 A217224 * A055605 A217342 A319519

Adjacent sequences: A272033 A272034 A272035 * A272037 A272038 A272039

Keyword

nonn

Author

Michel Marcus, Apr 18 2016

Status

approved