Search: id:A130245
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%I A130245
%S A130245 0,1,2,3,4,4,4,5,5,5,5,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,
%T A130245 8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,
%U A130245 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 A130245 Number of Lucas numbers (A000032) <= n.
%C A130245 Partial sums of the Lucas indicator sequence A102460. For n>=2, we have 
               a(A000032(n))=n+1.
%F A130245 a(n)=1+floor(log_phi((n+sqr(n^2+4))/2))=1+floor(arsinh(n/2)/ln(phi)) 
               for n>=2, where phi=(1+sqr(5))/2.
%F A130245 a(n)=A130241(n)+1=A130242(n+1) for n>=2.
%F A130245 G.f.: g(x)=1/(1-x)*sum{k>=0, x^Lucas(k)}.
%F A130245 a(n)=1+floor(log_phi(n+1/2)) for n>=1, where phi is the golden ratio.
%e A130245 a(9)=5 because there are 5 Lucas numbers <=9 (2,1,3,4 and 7).
%Y A130245 For partial sums see A130246. Other related sequences: A000032, A130241, 
               A130242, A130247, A130249, A130253, A130255, A130259. Indicator sequence 
               A102460. Fibonacci inverse see A130233 - A130240, A104162, A108852.
%Y A130245 Sequence in context: A087827 A136528 A130242 this_sequence A087793 A030411 
               A132913
%Y A130245 Adjacent sequences: A130242 A130243 A130244 this_sequence A130246 A130247 
               A130248
%K A130245 nonn
%O A130245 0,3
%A A130245 Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 19 2007, Jul 02 
               2007

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