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A072601
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Numbers which in base 2 have at least as many 1's as 0's.
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7
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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, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 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
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refs;
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history;
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OFFSET
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1,2
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..5370 (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.
Index entries for sequences related to binary expansion of n
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EXAMPLE
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8 = 1000_2 is not present (one '1', three '0's).
10 is present because 10=1010_2 contains 2 '0's and 2 '1's: 2<=2;
11 is present because 11=1011_2 contains 1 '0' and 3 '1's: 1<=3.
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MATHEMATICA
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geQ[n_] := Module[{a, b}, {a, b} = DigitCount[n, 2]; a >= b]; Select[Range[103], geQ] (* T. D. Noe, Apr 20 2013 *)
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PROG
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(Haskell)
a072601 n = a072601_list !! (n-1)
a072601_list = filter ((<= 0) . a037861) [0..]
-- Reinhard Zumkeller, Aug 01 2013
(PARI) is(n)=2*hammingweight(n)>exponent(n) \\ Charles R Greathouse IV, Apr 18 2020
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CROSSREFS
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Cf. A007088, A000120, A023416, A061854.
Cf. A037861(a(n)) <= 0.
Cf. A072600 (#0's < #1's), this seq (#0's <= #1's), A031443 (#0's = #1's).
Cf. A072602 (#0's >= #1's), A072603 (#0's > #1's), A044951 (#0's <> #1's).
Sequence in context: A166937 A039250 A135130 * A039192 A188087 A329133
Adjacent sequences: A072598 A072599 A072600 * A072602 A072603 A072604
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KEYWORD
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nonn,base,easy
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AUTHOR
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Reinhard Zumkeller, Jun 23 2002
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STATUS
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approved
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