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

1,1

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

Example

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.

Mathematica

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

Prog

(Haskell)
a072602 n = a072602_list !! (n-1)
a072602_list = filter ((>= 0) . a037861) [1..]
-- Reinhard Zumkeller, Mar 31 2015
(PARI) is(n)=2*hammingweight(n)<=exponent(n)+1 \\ Charles R Greathouse IV, Apr 18 2020

Crossrefs

Cf. A007088, A000120, A023416, A072600, A072601, A031443, A072603.

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

Sequence in context: A352831 A047466 A003485 * A374664 A049642 A326713

Adjacent sequences: A072599 A072600 A072601 * A072603 A072604 A072605

Keyword

nonn,base,easy

Author

Reinhard Zumkeller, Jun 23 2002

Extensions

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

Status

approved