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A272036
Numbers n such that the sum of the inverse of the exponents in the binary expansion of 2n is equal to 1.
6
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
KEYWORD
nonn
AUTHOR
Michel Marcus, Apr 18 2016
STATUS
approved