A072601 - OEIS

%I #41 Aug 12 2023 17:20:57

%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,

%T 37,38,39,41,42,43,44,45,46,47,49,50,51,52,53,54,55,56,57,58,59,60,61,

%U 62,63,71,75,77,78,79,83,85,86,87,89,90,91,92,93,94,95,99,101,102,103

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

%H T. D. Noe, <a href="/A072601/b072601.txt">Table of n, a(n) for n = 1..5370</a> (numbers < 2^13)

%H 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 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 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%e 8 = 1000_2 is not present (one '1', three '0's).

%e 10 is present because 10=1010_2 contains 2 '0's and 2 '1's: 2<=2;

%e 11 is present because 11=1011_2 contains 1 '0' and 3 '1's: 1<=3.

%t geQ[n_] := Module[{a, b}, {a, b} = DigitCount[n, 2]; a >= b]; Select[Range[103], geQ] (* _T. D. Noe_, Apr 20 2013 *)

%t Select[Range[110],DigitCount[#,2,1]>=DigitCount[#,2,0]&] (* _Harvey P. Dale_, Aug 12 2023 *)

%o (Haskell)

%o a072601 n = a072601_list !! (n-1)

%o a072601_list = filter ((<= 0) . a037861) [0..]

%o -- _Reinhard Zumkeller_, Aug 01 2013

%o (PARI) is(n)=2*hammingweight(n)>exponent(n) \\ _Charles R Greathouse IV_, Apr 18 2020

%Y Cf. A007088, A000120, A023416, A061854.

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

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

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

%K nonn,base,easy

%O 1,2

%A _Reinhard Zumkeller_, Jun 23 2002