%I A130241
%S A130241 1,1,2,3,3,3,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,
%T A130241 7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
%U A130241 8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9
%N A130241 Maximal index k of a Lucas number such that Lucas(k)<=n (the 'lower' 
               Lucas (A000032) Inverse).
%C A130241 Inverse of the Lucas sequence (A000032), nearly, since a(Lucas(n))=n 
               for n>=1 (see A130242 and A130247 for other versions). For n>=2, 
               a(n)+1 is equal to the partial sum of the Lucas indicator sequence 
               (see A102460). Identical to A130247 except for n=2.
%F A130241 a(n)=floor(log_phi((n+sqr(n^2+4))/2))=floor(arsinh(n/2)/ln(phi)) where 
               phi=(1+sqr(5))/2.
%F A130241 a(n)=A130242(n+1)-1 for n>=2. a(n)=A130247(n) except for n=2.
%F A130241 G.f.: g(x)=1/(1-x)*sum{k>=1, x^Lucas(k)}.
%F A130241 a(n)=floor(log_phi(n+1/2)) for n>=2, where phi is the golden ratio.
%e A130241 a(10)=4, since Lucas(4)=7<=10 but Lucas(5)=11>10.
%Y A130241 For partial sums see A130243. Other related sequences: A000032, A130242, 
               A130245, A130247, A130249, A130255, A130259. Indicator sequence A102460. 
               Fibonacci inverse see A130233 - A130240, A104162.
%Y A130241 Sequence in context: A103586 A117806 A085423 this_sequence A130247 A087839 
               A106742
%Y A130241 Adjacent sequences: A130238 A130239 A130240 this_sequence A130242 A130243 
               A130244
%K A130241 nonn
%O A130241 1,3
%A A130241 Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 19 2007, Jul 02 
               2007