%I A130259
%S A130259 0,1,1,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,
%T A130259 4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,
%U A130259 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5
%N A130259 Maximal index k of an even Fibonacci number (A001906) such that A001906(k)=Fib(2k)<=n 
               (the 'lower' even Fibonacci Inverse).
%C A130259 Inverse of the even Fibonacci sequence (A001906), since a(A001906(n))=n 
               (see A130260 for another version). a(n)+1 is the number of even Fibonacci 
               numbers (A001906) <=n.
%F A130259 a(n)=floor(arsinh(sqr(5)*n/2)/(2*ln(phi))), where phi=(1+sqr(5))/2.
%F A130259 a(n)=A130260(n+1)-1.
%F A130259 G.f.: g(x)=1/(1-x)*sum(k>=1, x^Fib(2k)).
%F A130259 a(n)=floor(1/2*log_phi(sqr(5)*n+1)) for n>=0.
%e A130259 a(10)=3 because A001906(3)=8<=10, but A001906(4)=21>10.
%Y A130259 Cf. partial sums A130261. Other related sequences: A000045, A001519, 
               A130233, A130237, A130239, A130255, A130260, A104160. Lucas inverse: 
               A130241 - A130248.
%Y A130259 Sequence in context: A077430 A105513 A004233 this_sequence A068549 A132173 
               A023968
%Y A130259 Adjacent sequences: A130256 A130257 A130258 this_sequence A130260 A130261 
               A130262
%K A130259 nonn
%O A130259 0,4
%A A130259 Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 25 2007, Jul 02 
               2007