cp's OEIS Frontend

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.

%I A036994 #34 Sep 16 2022 08:55:36
%S A036994 1,3,7,11,15,23,27,31,39,43,47,55,59,63,79,87,91,95,103,107,111,119,
%T A036994 123,127,143,151,155,159,167,171,175,183,187,191,207,215,219,223,231,
%U A036994 235,239,247,251,255,287,303,311,315,319,335,343,347,351,359,363,367
%N 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.
%C A036994 Even numbers can't appear in this sequence. - _Alonso del Arte_, Sep 21 2011
%H A036994 Reinhard Zumkeller, <a href="/A036994/b036994.txt">Table of n, a(n) for n = 1..10000</a>
%H A036994 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%t A036994 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 *)
%t A036994 Select[Range[400],Min[Accumulate[Reverse[IntegerDigits[#,2]/. (0->-1)]]]> 0&] (* _Harvey P. Dale_, Apr 23 2016 *)
%o A036994 (Haskell)
%o A036994 a036994 n = a036994_list !! (n-1)
%o A036994 a036994_list = filter ((p 0) . a030308_row) [1, 3 ..] where
%o A036994    p ones []    = ones > 0
%o A036994    p ones (0:bs) = ones > 1 && p (ones - 1) bs
%o A036994    p ones (1:bs) = p (ones + 1) bs
%o A036994 -- _Reinhard Zumkeller_, Aug 01 2013
%o A036994 (Python)
%o A036994 from itertools import count, islice
%o A036994 def A036994_gen(startvalue=0): # generator of terms >= startvalue
%o A036994     for n in count(max(startvalue,0)):
%o A036994         s = bin(n)[2:]
%o A036994         c, l = 0, len(s)
%o A036994         for i in range(l):
%o A036994             c += int(s[l-i-1])
%o A036994             if 2*c <= i + 1:
%o A036994                 break
%o A036994         else:
%o A036994             yield n
%o A036994 A036994_list = list(islice(A036994_gen(),20)) # _Chai Wah Wu_, Dec 31 2021
%o A036994 (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
%Y A036994 Cf. A036990, A036991, A036992, A036993.
%Y A036994 Cf. A030308.
%K A036994 nonn,easy,base
%O A036994 1,2
%A A036994 _N. J. A. Sloane_
%E A036994 More terms from _Erich Friedman_