A044951 Numbers having a different number of ones and zeros in base 2.

1, 3, 4, 5, 6, 7, 8, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 39, 40, 43, 45, 46, 47, 48, 51, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77

Offset

1,2

Links

Michael De Vlieger, Table of n, a(n) for n = 1..14031 (all terms k <= 2^14).

Jason Bell, Thomas Finn Lidbetter, and Jeffrey Shallit, Additive Number Theory via Approximation by Regular Languages, arXiv:1804.07996 [cs.FL], 2018.

Thomas Finn Lidbetter, Counting, Adding, and Regular Languages, Master's Thesis, University of Waterloo, Ontario, Canada, 2018.

Index entries for sequences related to binary expansion of n

Formula

a(n) ~ n. - Charles R Greathouse IV, Apr 18 2020

Example

From Michael De Vlieger, Feb 07 2019: (Start)
11 (binary 1011) has more 1's than 0's, thus it is in the sequence.
12 (binary 1100) has an equal number of 0's and 1's, thus it is not in the sequence.
(End)

Mathematica

Select[Range@ 77, UnsameQ @@ DigitCount[#, 2] &] (* Michael De Vlieger, Feb 07 2019 *)

Prog

(PARI) is(n)=2*hammingweight(n)!=exponent(n)+1 \\ Charles R Greathouse IV, Apr 18 2020

Crossrefs

Cf. A072600 (#0's < #1's), A072601 (#0's <= #1's), A031443 (#0's = #1's).

Cf. A072602 (#0's >= #1's), A072603 (#0's > #1's), this sequence (#0's <> #1's).

Sequence in context: A261604 A120561 A051016 * A138308 A039084 A277641

Adjacent sequences: A044948 A044949 A044950 * A044952 A044953 A044954

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved