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A004761
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Numbers n whose binary expansion does not begin with 11.
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10
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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
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OFFSET
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1,3
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LINKS
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FORMULA
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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
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
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MAPLE
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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:
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MATHEMATICA
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Select[Range[0, 140], # <= 2 || Take[IntegerDigits[#, 2], 2] != {1, 1} &] (* Michael De Vlieger, Aug 03 2016 *)
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PROG
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(PARI) a(n) = if(n<=2, n-1, n-=2; n + 1<<logint(n, 2)); \\ Kevin Ryde, Apr 14 2021
(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)))
(Python)
def A004761(n): return m+(1<<m.bit_length()-1) if (m:=n-2) else n-1 # Chai Wah Wu, Jul 26 2023
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CROSSREFS
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Apart from initial terms, same as A004754.
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KEYWORD
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nonn,easy,base
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AUTHOR
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STATUS
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approved
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