Search: id:A010056
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%I A010056
%S A010056 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,
%T A010056 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,
%U A010056 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
%N A010056 a(n) = 1 if n is a Fibonacci number, otherwise 0.
%C A010056 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
%C A010056 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
%H A010056 <a href="Sindx_Ch.html#char_fns">Index entries for characteristic functions</
               a>
%H A010056 D. Bailey et al., <a href="http://crd.lbl.gov/~dhbailey/dhbpapers/algebraic.pdf">
               On the binary expansions of algebraic numbers</a>
%F A010056 G.f.: g(x)=sum{k>=0, x^Fib/k)}-x. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), 
               May 17 2007
%Y A010056 Cf. A000045, A084119, A124091.
%Y A010056 Cf. A104162, A108852, A130233, A130234.
%Y A010056 Decimal expansion of Fibonacci binary is in A084119.
%Y A010056 Sequence in context: A121802 A156241 A156254 this_sequence A155898 A115952 
               A115524
%Y A010056 Adjacent sequences: A010053 A010054 A010055 this_sequence A010057 A010058 
               A010059
%K A010056 nonn
%O A010056 0,1
%A A010056 N. J. A. Sloane (njas(AT)research.att.com).

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