A072601 Numbers which in base 2 have at least as many 1's as 0's.

1, 2, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 19, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 71, 75, 77, 78, 79, 83, 85, 86, 87, 89, 90, 91, 92, 93, 94, 95, 99, 101, 102, 103

Offset

1,2

Links

T. D. Noe, Table of n, a(n) for n = 1..5370 (numbers < 2^13)

Jason Bell, Thomas Finn Lidbetter, 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

Example

8 = 1000_2 is not present (one '1', three '0's).
10 is present because 10=1010_2 contains 2 '0's and 2 '1's: 2<=2;
11 is present because 11=1011_2 contains 1 '0' and 3 '1's: 1<=3.

Mathematica

geQ[n_] := Module[{a, b}, {a, b} = DigitCount[n, 2]; a >= b]; Select[Range[103], geQ] (* T. D. Noe, Apr 20 2013 *)
Select[Range[110], DigitCount[#, 2, 1]>=DigitCount[#, 2, 0]&] (* Harvey P. Dale, Aug 12 2023 *)

Prog

(Haskell)
a072601 n = a072601_list !! (n-1)
a072601_list = filter ((<= 0) . a037861) [0..]
-- Reinhard Zumkeller, Aug 01 2013
(PARI) is(n)=2*hammingweight(n)>exponent(n) \\ Charles R Greathouse IV, Apr 18 2020

Crossrefs

Cf. A007088, A000120, A023416, A061854.

Cf. A037861(a(n)) <= 0.

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

Cf. A072602 (#0's >= #1's), A072603 (#0's > #1's), A044951 (#0's <> #1's).

Sequence in context: A166937 A039250 A135130 * A039192 A188087 A329133

Adjacent sequences: A072598 A072599 A072600 * A072602 A072603 A072604

Keyword

nonn,base,easy

Author

Reinhard Zumkeller, Jun 23 2002

Status

approved