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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
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, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..104.

FORMULA

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.

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

EXAMPLE

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

CROSSREFS

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

Sequence in context: A318781 A316844 A331245 * A091092 A218461 A186189

Adjacent sequences:  A130236 A130237 A130238 * A130240 A130241 A130242

KEYWORD

nonn

AUTHOR

Hieronymus Fischer, May 17 2007, May 28 2007

STATUS

approved

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Last modified June 16 20:29 EDT 2021. Contains 345068 sequences. (Running on oeis4.)