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A130239 Maximal index k of the square of a Fibonacci number such that Fib(k)^2 <= n (the 'lower' squared Fibonacci Inverse). 9

%I

%S 0,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,

%T 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,

%U 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6

%N Maximal index k of the square of a Fibonacci number such that Fib(k)^2 <= n (the 'lower' squared Fibonacci Inverse).

%F a(n)=max(k | Fib(k)^2<=n)=A130233(floor(sqrt(n)))=floor(arcsinh(sqrt(5n)/2)/log(phi)) where phi=(1+sqrt(5))/2.

%F G.f.: g(x)=1/(1-x)*sum{k>=1, x^(Fib(k)^2)}.

%e a(10)=4 since Fib(4)^2=9<=10 but Fib(5)^2=25>10.

%Y Partial sums: A130240. Other related sequences: A000045, A130233, A130234, A130235, A130236, A130237, A130238, A130240, A130243, A130246, A130248, A130239, A130251, A130253, A130257, A130261.

%K nonn

%O 0,2

%A _Hieronymus Fischer_, May 17 2007, May 28 2007

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Last modified July 24 01:41 EDT 2021. Contains 346269 sequences. (Running on oeis4.)