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Search: id:A010056
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| A010056 |
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a(n) = 1 if n is a Fibonacci number, otherwise 0. |
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+0
10
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| 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Understood as a binary number, sum(k>=0, a(k)/2^k), the resulting decimal expansion is 1.910278797207865891... = Fibonacci_binary+0.5 (see A084119) or Fibonacci_binary_constant-0.5 (see A124091), respectively. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 14 2007
a(n)=1 if and only if there is an integer m such that x=n is a root of p(x)=25*x^4-10*m^2*x^2+m^4-16. Also a(n)=1 iff floor(s)<>floor(c) or ceiling(s)<>ceiling(c) where s=arsinh(sqr(5)*n/2)/ln(phi), c=arcosh(sqr(5)*n/2)/ln(phi) and phi=(1+sqr(5))/2. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 17 2007
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LINKS
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Index entries for characteristic functions
D. Bailey et al., On the binary expansions of algebraic numbers
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FORMULA
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G.f.: g(x)=sum{k>=0, x^Fib/k)}-x. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 17 2007
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CROSSREFS
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Cf. A000045, A084119, A124091.
Cf. A104162, A108852, A130233, A130234.
Decimal expansion of Fibonacci binary is in A084119.
Adjacent sequences: A010053 A010054 A010055 this_sequence A010057 A010058 A010059
Sequence in context: A121802 A156241 A156254 this_sequence A155898 A115952 A115524
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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