A004765 Numbers whose binary expansion does not begin 111.

0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83

Offset

1,3

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

a(1) = 0, a(2) = 1, a(3) = 2, a(4) = 3, a(2^(m+1)+2^m+k+2) = 2^(m+2) + k, m >= 0, 0 <= k < (2^(m+1)+2^m). - Yosu Yurramendi, Aug 08 2016

From Robert Israel, Aug 08 2016: (Start)

For n >= 5, a(2n-2) = 2 a(n) and a(2n-1) = 2 a(n)+1.

G.f. g(x) satisfies g(x) - (2/x + 2/x^2)*g(x^2) = -x^2 - x^4 - x^6 + x^9/(1-x^2). (End)

Maple

f:= proc(n) option remember;
   if n < 8 then n-1
   else 2*procname(floor((n+2)/2))+(n mod 2)
   fi
end proc:
map(f, [$1..100]); # Robert Israel, Aug 08 2016

Mathematica

w = {1, 1, 1}; Select[Range[0, 83], If[# < 2^(Length@ w - 1), True, Take[IntegerDigits[#, 2], Length@ w] != w] &] (* Michael De Vlieger, Aug 08 2016 *)

Prog

(Haskell)
a004765 n = a004765_list !! n
a004765_list = filter f [0..] where
   f x | x <= 8    = x /= 7
       | otherwise = f (x `div` 2)
-- Reinhard Zumkeller, Jun 03 2012

Crossrefs

Cf. A007088.

Sequence in context: A356939 A113619 A325114 * A247063 A003726 A343110

Adjacent sequences: A004762 A004763 A004764 * A004766 A004767 A004768

Keyword

nonn,easy,base

Author

N. J. A. Sloane

Status

approved