Search: id:A130256
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%I A130256
%S A130256 0,0,2,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,
%T A130256 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
%U A130256 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7
%N A130256 Minimal index k of an odd Fibonacci number A001519 such that A001519(k)=Fib(2k-1)>
               =n (the 'upper' odd Fibonacci Inverse).
%C A130256 Inverse of the odd Fibonacci sequence (A001519), nearly, since a(A001519(n))=n 
               except for n=1 (see A130255 for another version). a(n+1) is the number 
               of odd Fibonacci numbers (A001519) <=n (for n>=0).
%F A130256 a(n)=ceiling((1+arcosh(sqr(5)*n/2)/ln(phi))/2).
%F A130256 G.f.: g(x)=x/(1-x)*sum(k>=0, x^Fib(2k-1)).
%F A130256 a(n)=ceiling(1/2*(1+log_phi(sqr(5)*n-1))) for n>=2, where phi=(1+sqr(5))/
               2.
%e A130256 a(10)=4 because A001519(4)=13>=10, but A001519(3)=5<10.
%Y A130256 Cf. partial sums A130258. Other related sequences: A000045, A001906, 
               A130234, A130237, A130239, A130255, A130260. Lucas inverse: A130241 
               - A130248.
%Y A130256 Sequence in context: A084516 A084526 A081288 this_sequence A103586 A117806 
               A085423
%Y A130256 Adjacent sequences: A130253 A130254 A130255 this_sequence A130257 A130258 
               A130259
%K A130256 nonn
%O A130256 0,3
%A A130256 Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 24 2007, Jul 02 
               2007

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