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

%I A072602 #32 Apr 18 2020 01:02:07
%S A072602 2,4,8,9,10,12,16,17,18,20,24,32,33,34,35,36,37,38,40,41,42,44,48,49,
%T A072602 50,52,56,64,65,66,67,68,69,70,72,73,74,76,80,81,82,84,88,96,97,98,
%U A072602 100,104,112,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142
%N A072602 Numbers such that in base 2 the number of 0's is >= the number of 1's.
%H A072602 T. D. Noe, <a href="/A072602/b072602.txt">Table of n, a(n) for n = 1..7555</a> (numbers up to 2^14)
%H A072602 Jason Bell, Thomas Finn Lidbetter, Jeffrey Shallit, <a href="https://arxiv.org/abs/1804.07996">Additive Number Theory via Approximation by Regular Languages</a>, arXiv:1804.07996 [cs.FL], 2018.
%H A072602 Thomas Finn Lidbetter, <a href="https://uwspace.uwaterloo.ca/bitstream/handle/10012/14254/Lidbetter_Thomas.pdf">Counting, Adding, and Regular Languages</a>, Master's Thesis, University of Waterloo, Ontario, Canada, 2018.
%H A072602 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%e A072602 8 is present because '1000' contains 3 '0's and 1 '1': 3 >= 1;
%e A072602 9 is present because '1001' contains 2 '0's and 2 '1's: 2 >= 2.
%t A072602 Select[Range[150],DigitCount[#,2,0]>=DigitCount[#,2,1]&] (* _Harvey P. Dale_, May 09 2012 *)
%o A072602 (Haskell)
%o A072602 a072602 n = a072602_list !! (n-1)
%o A072602 a072602_list = filter ((>= 0) . a037861) [1..]
%o A072602 -- _Reinhard Zumkeller_, Mar 31 2015
%o A072602 (PARI) is(n)=2*hammingweight(n)<=exponent(n)+1 \\ _Charles R Greathouse IV_, Apr 18 2020
%Y A072602 Cf. A007088, A000120, A023416, A072600, A072601, A031443, A072603.
%Y A072602 Cf. A037861(a(n)) >= 0.
%K A072602 nonn,base,easy
%O A072602 1,1
%A A072602 _Reinhard Zumkeller_, Jun 23 2002
%E A072602 Edited by _N. J. A. Sloane_, Jun 23 2009