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

1,3

Links

Table of n, a(n) for n=1..68.

L. Sze, Sequence 102

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

Mathematica

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

Crossrefs

Complementary to A004756.

Cf. A099396.

Sequence in context: A349019 A225354 A166111 * A061854 A367861 A214432

Adjacent sequences: A004759 A004760 A004761 * A004763 A004764 A004765

Keyword

nonn,easy,base

Author

N. J. A. Sloane

Status

approved