A036994 Numbers k with the property that reading from right to left in the binary expansion of k, the number of 1's always stays ahead of the number of 0's.

1, 3, 7, 11, 15, 23, 27, 31, 39, 43, 47, 55, 59, 63, 79, 87, 91, 95, 103, 107, 111, 119, 123, 127, 143, 151, 155, 159, 167, 171, 175, 183, 187, 191, 207, 215, 219, 223, 231, 235, 239, 247, 251, 255, 287, 303, 311, 315, 319, 335, 343, 347, 351, 359, 363, 367

Offset

1,2

Comments

Even numbers can't appear in this sequence. - Alonso del Arte, Sep 21 2011

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for sequences related to binary expansion of n

Mathematica

aheadOnesRLQ[n_Integer] := Module[{digits, len, flag = True, iter = 1, ones = 0, zeros = 0}, digits = Reverse[IntegerDigits[n, 2]]; len = Length[digits]; While[flag && iter < len, If[digits[[iter]] == 1, ones++, zeros++]; flag = ones > zeros; iter++]; flag]; Select[Range[1, 201, 2], aheadOnesRLQ] (* Alonso del Arte, Sep 21 2011 *)
Select[Range[400], Min[Accumulate[Reverse[IntegerDigits[#, 2]/. (0->-1)]]]> 0&] (* Harvey P. Dale, Apr 23 2016 *)

Prog

(Haskell)
a036994 n = a036994_list !! (n-1)
a036994_list = filter ((p 0) . a030308_row) [1, 3 ..] where
   p ones []    = ones > 0
   p ones (0:bs) = ones > 1 && p (ones - 1) bs
   p ones (1:bs) = p (ones + 1) bs
-- Reinhard Zumkeller, Aug 01 2013
(Python)
from itertools import count, islice
def A036994_gen(startvalue=0): # generator of terms >= startvalue
    for n in count(max(startvalue, 0)):
        s = bin(n)[2:]
        c, l = 0, len(s)
        for i in range(l):
            c += int(s[l-i-1])
            if 2*c <= i + 1:
                break
        else:
            yield n
A036994_list = list(islice(A036994_gen(), 20)) # Chai Wah Wu, Dec 31 2021
(PARI) ok(x)={if(x<1, return(0)); my(c=logint(x, 2), c0=0, c1=0); for(i=0, c, if(bittest(x, i), c1++, c0++); if(c1<=c0, return(0))); 1} \\ for(n=1, 367, if(ok(n), print1(n, ", "))) - Ruud H.G. van Tol, Sep 14 2022

Crossrefs

Cf. A036990, A036991, A036992, A036993.

Cf. A030308.

Sequence in context: A246521 A160785 A095100 * A243115 A279106 A172306

Adjacent sequences: A036991 A036992 A036993 * A036995 A036996 A036997

Keyword

nonn,easy,base

Author

N. J. A. Sloane

Extensions

More terms from Erich Friedman

Status

approved