A004762 - OEIS

%I #24 Feb 12 2021 05:35:05

%S 0,1,2,3,5,6,7,10,11,12,13,14,15,20,21,22,23,24,25,26,27,28,29,30,31,

%T 40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,

%U 63,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98

%N Numbers whose binary expansion does not begin 100.

%H L. Sze, <a href="https://web.archive.org/web/20050426082410/http://lsze.cosam.calpoly.edu/sequence102.pdf">Sequence 102</a>

%F a(n+1) = n + 2^A099396(n).

%F G.f.: x/(1-x)^2 + x/(1-x) * Sum[k>=0, 2^k*x^(3*2^k)].

%F a(1) = 0, a(2) = 1, a(3) = 2, a(4) = 3, a(2^(m+1) + 2^m + k + 2) = 2^(m+2) + 2^m + k, m >= 0, 0 <= k < (2^(m+1) + 2^m). - _Yosu Yurramendi_, Aug 08 2016

%t Join[{0,1,2,3},Select[Range[4,100],Take[IntegerDigits[#,2],3]!={1,0,0}&]] (* _Harvey P. Dale_, Feb 02 2015 *)

%Y Complementary to A004756.

%Y Cf. A099396.

%K nonn,easy,base

%O 1,3

%A _N. J. A. Sloane_