A130239 - OEIS

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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).

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; internal format)

	OFFSET	`0,2`
	FORMULA	`a(n)=max(k \| Fib(k)^2<=n)=A130233(floor(sqr(n)))=floor(arsinh(sqr(5n)/2)/ln(phi)) where phi=(1+sqr(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: A072358 A074795 A069577 * A091092 A186189 A083375` `Adjacent sequences: A130236 A130237 A130238 * A130240 A130241 A130242`
	KEYWORD	`nonn`
	AUTHOR	`Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 17 2007, May 28 2007`

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Last modified February 16 16:25 EST 2012. Contains 205938 sequences.