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Maximal index k of an even Fibonacci number (A001906) such that A001906(k)=Fib(2k)<=n (the 'lower' even Fibonacci Inverse).

+0
10

0, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 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, 5, 5, 5, 5, 5, 5, 5 (list; graph; listen)

	OFFSET	`0,4`
	COMMENT	`Inverse of the even Fibonacci sequence (A001906), since a(A001906(n))=n (see A130260 for another version). a(n)+1 is the number of even Fibonacci numbers (A001906) <=n.`
	FORMULA	`a(n)=floor(arsinh(sqr(5)n/2)/(2ln(phi))), where phi=(1+sqr(5))/2.` `a(n)=A130260(n+1)-1.` `G.f.: g(x)=1/(1-x)sum(k>=1, x^Fib(2k)).` `a(n)=floor(1/2log_phi(sqr(5)*n+1)) for n>=0.`
	EXAMPLE	`a(10)=3 because A001906(3)=8<=10, but A001906(4)=21>10.`
	CROSSREFS	`Cf. partial sums A130261. Other related sequences: A000045, A001519, A130233, A130237, A130239, A130255, A130260, A104160. Lucas inverse: A130241 - A130248.` `Sequence in context: A077430 A105513 A004233 this_sequence A068549 A132173 A023968` `Adjacent sequences: A130256 A130257 A130258 this_sequence A130260 A130261 A130262`
	KEYWORD	`nonn`
	AUTHOR	`Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 25 2007, Jul 02 2007`

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Last modified July 25 07:41 EDT 2008. Contains 142293 sequences.

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