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

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• base

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

Crossrefs

Cf. A036990, A036991, A036992, A036993.

Cf. A030308.

Programs

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

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 *)

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

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

Extensions

More terms from Erich Friedman