A072602 Numbers such that in base 2 the number of 0's is >= the number of 1's.

2, 4, 8, 9, 10, 12, 16, 17, 18, 20, 24, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 44, 48, 49, 50, 52, 56, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 76, 80, 81, 82, 84, 88, 96, 97, 98, 100, 104, 112, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142

Offset: 1

Author

Reinhard Zumkeller, Jun 23 2002

Keywords

• nonn
• base
• easy

Examples

			8 is present because '1000' contains 3 '0's and 1 '1': 3 >= 1;
9 is present because '1001' contains 2 '0's and 2 '1's: 2 >= 2.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..7555 (numbers up to 2^14)
• 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, A072600, A072601, A031443, A072603.

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

Programs

Haskell

a072602 n = a072602_list !! (n-1)
a072602_list = filter ((>= 0) . a037861) [1..]
-- Reinhard Zumkeller, Mar 31 2015

Mathematica

Select[Range[150],DigitCount[#,2,0]>=DigitCount[#,2,1]&] (* Harvey P. Dale, May 09 2012 *)

PARI

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

Extensions

Edited by N. J. A. Sloane, Jun 23 2009