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

Author

Clark Kimberling

Keywords

• nonn
• base
• easy

Examples

			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)
		

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

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).

Programs

Mathematica

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

PARI

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

Formula

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