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A036990
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Numbers n such that, in the binary expansion of n, reading from right to left, the number of 1's never exceeds the number of 0's.
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10
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0, 2, 4, 8, 10, 12, 16, 18, 20, 24, 32, 34, 36, 40, 42, 44, 48, 50, 52, 56, 64, 66, 68, 72, 74, 76, 80, 82, 84, 88, 96, 98, 100, 104, 112, 128, 130, 132, 136, 138, 140, 144, 146, 148, 152, 160, 162, 164, 168, 170, 172, 176, 178, 180, 184, 192, 194, 196, 200, 202, 204
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OFFSET
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1,2
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COMMENTS
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A036989(a(n)) = 1. - Reinhard Zumkeller, Jul 31 2013
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
H. Niederreiter and M. Vielhaber, Tree complexity and a doubly exponential gap between structured and random sequences, J. Complexity, 12 (1996), 187-198.
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FORMULA
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a(n) = 2*A095775(n). - Robert G. Wilson v
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MATHEMATICA
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fQ[n_] := Block[{od = ev = k = 0, id = Reverse@IntegerDigits[n, 2], lmt = Floor@Log[2, n] + 1}, While[k < lmt && od < ev + 1, If[OddQ@id[[k + 1]], od++, ev++ ]; k++ ]; If[k == lmt && od < ev + 1, True, False]]; Select[ Range[0, 204, 2], fQ@# &] (* Robert G. Wilson v, Jan 11 2007 *)
(* b = A036989 *) b[0] = 1; b[n_?EvenQ] := b[n] = Max[b[n/2]-1, 1]; b[n_] := b[n] = b[(n-1)/2]+1; Select[Range[0, 300, 2], b[#] == 1 &] (* Jean-François Alcover, Nov 05 2013, after Reinhard Zumkeller *)
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PROG
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(Haskell)
a036990 n = a036990_list !! (n-1)
a036990_list = filter ((== 1) . a036989) [0..]
-- Reinhard Zumkeller, Jul 31 2013
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CROSSREFS
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Cf. A036988, A036991, A036992, A061854, A125086.
Each term is 2^n * some term of A014486 (n >= 0).
Cf. A030308.
Sequence in context: A047464 A189786 A195066 * A097498 A346502 A321580
Adjacent sequences: A036987 A036988 A036989 * A036991 A036992 A036993
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KEYWORD
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nonn,easy,base
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Erich Friedman.
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STATUS
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approved
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