id:A130239 - OEIS Search Results

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

+0
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; listen)

	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, A230234, A130235, A130236, A130237, A130238, A130240, A130243, A130246, A130248, A130239, A130251, A130253, A130257, A130261.` `Adjacent sequences: A130236 A130237 A130238 this_sequence A130240 A130241 A130242` `Sequence in context: A072358 A074795 A069577 this_sequence A091092 A083375 A088519`
	KEYWORD	`nonn`
	AUTHOR	`Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 17 2007, May 28 2007`

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Last modified October 7 14:39 EDT 2008. Contains 144666 sequences.

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