Search: id:A130260
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%I A130260
%S A130260 0,1,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,
%T A130260 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
%U A130260 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6
%N A130260 Minimal index k of an even Fibonacci number A001906 such that A001906(k)=Fib(2k)>
               =n (the 'upper' even Fibonacci Inverse).
%C A130260 Inverse of the even Fibonacci sequence (A001906), since a(A001906(n))=n 
               (see A130259 for another version). a(n+1) is the number of even Fibonacci 
               numbers (A001906) <=n.
%F A130260 a(n)=ceiling(arsinh(sqr(5)*n/2)/(2*ln(phi))) for n>=0.
%F A130260 a(n)=ceiling(arcosh(sqr(5)*n/2)/(2*ln(phi))) for n>=1.
%F A130260 a(n)=ceiling(log_phi(sqr(5)*n)/2)=ceiling(log_phi(sqr(5)*n-1)/2) for 
               n>=1, where phi=(1+sqr(5))/2.
%F A130260 a(n)=A130259(n-1)+1, for n>=1.
%F A130260 G.f.: g(x)=x/(1-x)*sum(k>=0, x^Fib(2k)).
%e A130260 a(10)=4 because A001906(4)=21>=10, but A001906(3)=8<10.
%Y A130260 Cf. partial sums A130262. Other related sequences: A000045, A001519, 
               A130234, A130237, A130239, A130256, A130259. Lucas inverse: A130241 
               - A130248.
%Y A130260 Sequence in context: A084320 A120699 A072643 this_sequence A111393 A062537 
               A097688
%Y A130260 Adjacent sequences: A130257 A130258 A130259 this_sequence A130261 A130262 
               A130263
%K A130260 nonn
%O A130260 0,3
%A A130260 Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 25 2007, May 28 
               2007, Jul 02 2007

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