A036990 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.

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

Offset

1,2

Comments

A036989(a(n)) = 1. - Reinhard Zumkeller, Jul 31 2013

Links

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.

Formula

a(n) = 2*A095775(n). - Robert G. Wilson v

Mathematica

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 *)

Prog

(Haskell)
a036990 n = a036990_list !! (n-1)
a036990_list = filter ((== 1) . a036989) [0..]
-- Reinhard Zumkeller, Jul 31 2013

Crossrefs

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

Keyword

nonn,easy,base

Author

N. J. A. Sloane.

Extensions

More terms from Erich Friedman.

Status

approved