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A004761 Numbers n whose binary expansion does not begin with 11. 9
0, 1, 2, 4, 5, 8, 9, 10, 11, 16, 17, 18, 19, 20, 21, 22, 23, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 128, 129 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a(1)=0, a(2)=1 and for k>1: a(2*k-1) = a(2*k-2)+1, a(2*k) = 2*a(k+1). - Reinhard Zumkeller, Jan 09 2002, corrected by Robert Israel, Mar 31 2017

For n > 0, a(n) = 1/2 * (4n - 3 - A006257(n-1)). - Ralf Stephan, Sep 16 2003

a(1) = 0, a(2) = 1, a(2^m+k+2) = 2^(m+1)+k, m >= 0, 0 <= k < 2^m. - Yosu Yurramendi, Jul 30 2016

a(2^m+k) = A004760(2^m+k) - 2^m, m >= 0, 0 <= k < 2^m. - Yosu Yurramendi, Aug 08 2016

G.f. g(x) satisfies g(x) = 2*(1+x)*g(x^2)/x^2 - x^2*(1-x^2-x^3)/(1-x^2). - Robert Israel, Mar 31 2017

MAPLE

f:= proc(n) option remember; if n::odd then procname(n-1)+1 else 2*procname(n/2+1) fi

end proc:

f(1):= 0: f(2):= 1:

map(f, [$1..100]); # Robert Israel, Mar 31 2017

MATHEMATICA

Select[Range[0, 140], # <= 2 || Take[IntegerDigits[#, 2], 2] != {1, 1} &] (* Michael De Vlieger, Aug 03 2016 *)

PROG

(PARI) is(n)=n^2==n || !binary(n)[2] \\ Charles R Greathouse IV, Mar 07 2013

(R)

maxrow <- 8 # by choice

b01 <- 1

for(m in 0:maxrow){

  b01 <- c(b01, rep(1, 2^(m+1))); b01[2^(m+1):(2^(m+1)+2^m-1)] <- 0

}

(a <- c(0, 1, which(b01 == 0)))

# Yosu Yurramendi, Mar 30 2017

CROSSREFS

Apart from initial terms, same as A004754.

Sequence in context: A175141 A072756 A325429 * A004754 A322014 A010450

Adjacent sequences:  A004758 A004759 A004760 * A004762 A004763 A004764

KEYWORD

nonn,easy,base

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified August 10 10:56 EDT 2020. Contains 336378 sequences. (Running on oeis4.)