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Minimal index k of an odd Fibonacci number A001519 such that A001519(k)=Fib(2k-1)>=n (the 'upper' odd Fibonacci Inverse).

+0
9

0, 0, 2, 3, 3, 3, 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, 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, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7 (list; graph; listen)

	OFFSET	`0,3`
	COMMENT	`Inverse of the odd Fibonacci sequence (A001519), nearly, since a(A001519(n))=n except for n=1 (see A130255 for another version). a(n+1) is the number of odd Fibonacci numbers (A001519) <=n (for n>=0).`
	FORMULA	`a(n)=ceiling((1+arcosh(sqr(5)n/2)/ln(phi))/2).` `G.f.: g(x)=x/(1-x)sum(k>=0, x^Fib(2k-1)).` `a(n)=ceiling(1/2(1+log_phi(sqr(5)n-1))) for n>=2, where phi=(1+sqr(5))/2.`
	EXAMPLE	`a(10)=4 because A001519(4)=13>=10, but A001519(3)=5<10.`
	CROSSREFS	`Cf. partial sums A130258. Other related sequences: A000045, A001906, A130234, A130237, A130239, A130255, A130260. Lucas inverse: A130241 - A130248.` `Adjacent sequences: A130253 A130254 A130255 this_sequence A130257 A130258 A130259` `Sequence in context: A084516 A084526 A081288 this_sequence A103586 A117806 A085423`
	KEYWORD	`nonn`
	AUTHOR	`Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 24 2007, Jul 02 2007`

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Last modified May 17 13:36 EDT 2008. Contains 139908 sequences.

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