Search: id:A102460
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%I A102460
%S A102460 0,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
%T A102460 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,
%U A102460 0,0,0,0,0,0,1
%N A102460 a(n) = 1 if n is a Lucas number, else a(n) = 0.
%C A102460 The number of nonnegative integer solutions to 25*x^4-10*n^2*x^2+n^4-16=0. 
               - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jul 02 2007
%C A102460 a(n)=1 if and only if there is an integer m such that x=n is a root of 
               p(x)=x^4-10*m^2*x^2+25*m^4-16. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), 
               Jul 02 2007
%C A102460 For n>=3: a(n)=1 iff floor(log_phi(n+1/2))=ceiling(log_phi(n-1/2)). - 
               Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jul 02 2007
%H A102460 <a href="Sindx_Ch.html#char_fns">Index entries for characteristic functions</
               a>
%H A102460 Casey Mongoven, <a href="http://caseymongoven.com/catalogue/b199.html">
               Lucas Binary no. 1</a>; electronic music created with this sequence.
%F A102460 G.f.: g(x)=sum{k>=0, x^A000032(k)}. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), 
               Jul 02 2007
%F A102460 a(n)=1+floor(arsinh(n/2)/ln(phi))-ceiling(arcosh(n/2)/ln(phi)) for n>
               =3, where phi=(1+sqr(5))/2. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), 
               Jul 02 2007
%F A102460 a(n)=1+A130241(n)-A130242(n) for n>=3. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), 
               Jul 02 2007
%F A102460 a(n)=1+A130247(n)-A130242(n) for n=>2. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), 
               Jul 02 2007
%F A102460 a(n)=A130245(n)-A130245(n-1) for n>=1. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), 
               Jul 02 2007
%F A102460 For n>=3: a(n)=1 iff A130241(n)=A130242(n). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), 
               Jul 02 2007
%Y A102460 Cf. A000032, A010056.
%Y A102460 Cf. partial sums A130245. Also A130241, A130242, A130247, A104162, A105348, 
               A000032.
%Y A102460 Sequence in context: A068344 A138886 A099859 this_sequence A080908 A131720 
               A131719
%Y A102460 Adjacent sequences: A102457 A102458 A102459 this_sequence A102461 A102462 
               A102463
%K A102460 nonn
%O A102460 0,1
%A A102460 Casey Mongoven (cm(AT)caseymongoven.com), Apr 18 2005

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