A130256 - OEIS

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A130256

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

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; refs; listen; history; text; internal format)

	OFFSET	`0,3`
	COMMENTS	`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).`
	LINKS	`Table of n, a(n) for n=0..100.`
	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.` `Sequence in context: A084516 A084526 A081288 * A103586 A194847 A117806` `Adjacent sequences: A130253 A130254 A130255 * A130257 A130258 A130259`
	KEYWORD	`nonn`
	AUTHOR	`Hieronymus Fischer, May 24 2007, Jul 02 2007`
	STATUS	`approved`

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Last modified May 23 16:56 EDT 2013. Contains 225610 sequences.