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

Author

Michel Marcus, Apr 18 2016

Keywords

• nonn

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

Examples

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

Links

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

Crossrefs

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

Programs

Mathematica

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

PARI

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