A272036 - OEIS

%I #33 Apr 06 2017 05:23:30

%S 1,38,2090,16902,18954,18988,131334,133386,133420,148258,150284,

%T 524314,524348,526386,541212,543250,543284,655644,657682,657716,

%U 672568,674580,8388742,8390794,8390828,8405666,8407692,8520098,8522124,8536962,8536996,8539048,8913052,8915090

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

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

%C Intersection of A272034 and A272035.

%C 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

%H Robert Israel, <a href="/A272036/b272036.txt">Table of n, a(n) for n = 1..1655</a> (first 200 terms from Peter Kagey)

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

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

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

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

%K nonn

%O 1,2

%A _Michel Marcus_, Apr 18 2016