A130259 - OEIS

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A130259

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

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; refs; listen; history; internal format)

	OFFSET	`0,4`
	COMMENTS	`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 * A068549 A132173 A023968` `Adjacent sequences: A130256 A130257 A130258 * 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 February 17 18:26 EST 2012. Contains 206065 sequences.