A004762 Numbers whose binary expansion does not begin 100.

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, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• base

Links

• L. Sze, Sequence 102

Crossrefs

Complementary to A004756.

Cf. A099396.

Programs

Mathematica

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

Formula

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

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

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