%I A130242
%S A130242 0,0,0,2,3,4,4,4,5,5,5,5,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,
%T A130242 8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,
%U A130242 9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10
%N A130242 Minimal index k of a Lucas number such that Lucas(k)>=n (the 'upper' 
               Lucas (A000032) Inverse).
%C A130242 Inverse of the Lucas sequence (A000032), nearly, since a(Lucas(n))=n 
               except for n=1 (see A130241 and A130247 for other versions). For 
               n>=2, a(n+1) is equal to the partial sum of the Lucas indicator sequence 
               (see A102460).
%F A130242 a(n)=ceiling(log_phi((n+sqr(n^2-4))/2))=ceiling(arcosh(n/2)/ln(phi)) 
               where phi=(1+sqr(5))/2.
%F A130242 a(n)=A130241(n-1)+1=A130245(n-1) for n>=3.
%F A130242 G.f.: g(x)=x/(1-x)*(2x^2+sum{k>=2, x^Lucas(k)}).
%F A130242 a(n)=ceiling(log_phi(n-1/2)) for n>=3, where phi is the golden ratio.
%e A130242 a(10)=5, since Lucas(5)=11>=10 but Lucas(4)=7<10.
%Y A130242 For partial sums see A130244. Other related sequences: A000032, A130241, 
               A130245, A130247, A130250, A130256, A130260. Indicator sequence A102460. 
               Fibonacci inverse see A130233 - A130240, A104162.
%Y A130242 Sequence in context: A064004 A087827 A136528 this_sequence A130245 A087793 
               A030411
%Y A130242 Adjacent sequences: A130239 A130240 A130241 this_sequence A130243 A130244 
               A130245
%K A130242 nonn
%O A130242 0,4
%A A130242 Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 19 2007, Jul 02 
               2007