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A004765 Numbers n such that binary expansion does not begin 111. 1
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 (list; graph; refs; listen; history; text; internal format)
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

Sequence in context: A302478 A113619 A325114 * A247063 A003726 A004828

Adjacent sequences:  A004762 A004763 A004764 * A004766 A004767 A004768

KEYWORD

nonn,easy,base

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified November 11 22:31 EST 2019. Contains 329046 sequences. (Running on oeis4.)