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 A072600 Numbers which in base 2 have fewer 0's than 1's. 10
 1, 3, 5, 6, 7, 11, 13, 14, 15, 19, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 39, 43, 45, 46, 47, 51, 53, 54, 55, 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, 105, 106, 107, 108, 109, 110, 111, 113, 114, 115 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A037861(a(n)) < 0. b_k = {a(n) | for all n s.t. a(n) contains k binary digits equal to 1} is the list of all valid win/loss round sequences in a "best of 2k-1" two player game, where 1 is a win and 0 is a loss. For example 19 = 10011b represents a game where the winner won the first two rounds, lost the next two, and won the last one. |b_k| = A001700(k). - Philippe Beaudoin, May 14 2014 LINKS T. D. Noe, Table of n, a(n) for n = 1..4733 ( 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. EXAMPLE 11 is present because '1011' contains 1 '0' and 3 '1's: 1<3. MATHEMATICA Select[Range[130], DigitCount[#, 2, 0]exponent(n)+1 \\ Charles R Greathouse IV, Apr 18 2020 CROSSREFS Cf. A007088, A000120, A023416, A072601, A031443, A072602, A072603, A037861 Sequence in context: A328557 A216782 A328952 * A047582 A333217 A301975 Adjacent sequences:  A072597 A072598 A072599 * A072601 A072602 A072603 KEYWORD nonn,base,easy AUTHOR Reinhard Zumkeller, Jun 23 2002 STATUS approved

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Last modified December 4 18:29 EST 2020. Contains 338936 sequences. (Running on oeis4.)