%I A130255
%S A130255 1,2,2,2,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,
%T A130255 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,
%U A130255 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6
%N A130255 Maximal index k of an odd Fibonacci number (A001519) such that A001519(k)=Fib(2k-1)<=n 
               (the 'lower' odd Fibonacci Inverse).
%C A130255 Inverse of the odd Fibonacci sequence (A001519), nearly, since a(A001519(n))=n 
               except for n=0 (see A130256 for another version). a(n)+1 is the number 
               of odd Fibonacci numbers (A001519) <=n (for n>=1).
%F A130255 a(n)=floor((1+arsinh(sqr(5)*n/2)/ln(phi))/2).
%F A130255 a(n)=floor((1+arcosh(sqr(5)*n/2)/ln(phi))/2).
%F A130255 a(n)=floor((1+log_phi(sqr(5)*n))/2) for n>=1, where phi=(1+sqr(5)/2.
%F A130255 G.f.: g(x)=1/(1-x)*sum(k>=1, x^Fib(2k-1)).
%F A130255 a(n)=floor(1/2*(1+log_phi(sqr(5)*n+1))) for n>=1.
%e A130255 a(10)=3 because A001519(3)=5<=10, but A001519(4)=13>10.
%Y A130255 Cf. partial sums A130257. Other related sequences: A000045, A130233, 
               A130237, A130239, A130256, A130259, A104160. Lucas inverse: A130241 
               - A130248.
%Y A130255 Sequence in context: A101787 A064099 A134021 this_sequence A082527 A132944 
               A106432
%Y A130255 Adjacent sequences: A130252 A130253 A130254 this_sequence A130256 A130257 
               A130258
%K A130255 nonn
%O A130255 1,2
%A A130255 Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 24 2007, Jul 02 
               2007