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

Author

Reinhard Zumkeller, Jun 23 2002

Keywords

• nonn
• base
• easy

Examples

			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.
		

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

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).

Programs

Haskell

a072601 n = a072601_list !! (n-1)
a072601_list = filter ((<= 0) . a037861) [0..]
-- Reinhard Zumkeller, Aug 01 2013

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 *)

PARI

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