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A130260 Minimal index k of an even Fibonacci number A001906 such that A001906(k) = Fib(2k) >= n (the 'upper' even Fibonacci Inverse). 6
0, 1, 2, 2, 3, 3, 3, 3, 3, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Inverse of the even Fibonacci sequence (A001906), since a(A001906(n))=n (see A130259 for another version). a(n+1) is the number of even Fibonacci numbers (A001906) <=n.

LINKS

Table of n, a(n) for n=0..100.

FORMULA

a(n)=ceiling(arcsinh(sqrt(5)*n/2)/(2*log(phi))) for n>=0.

a(n)=ceiling(arccosh(sqrt(5)*n/2)/(2*log(phi))) for n>=1.

a(n)=ceiling(log_phi(sqrt(5)*n)/2)=ceiling(log_phi(sqrt(5)*n-1)/2) for n>=1, where phi=(1+sqrt(5))/2.

a(n)=A130259(n-1)+1, for n>=1.

G.f.: g(x)=x/(1-x)*sum(k>=0, x^Fib(2k)).

EXAMPLE

a(10)=4 because A001906(4)=21>=10, but A001906(3)=8<10.

CROSSREFS

Cf. partial sums A130262. Other related sequences: A000045, A001519, A130234, A130237, A130239, A130256, A130259. Lucas inverse: A130241 - A130248.

Sequence in context: A161358 A120699 A072643 * A276621 A111393 A062537

Adjacent sequences:  A130257 A130258 A130259 * A130261 A130262 A130263

KEYWORD

nonn

AUTHOR

Hieronymus Fischer, May 25 2007, May 28 2007, Jul 02 2007

STATUS

approved

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Last modified February 19 08:54 EST 2018. Contains 299330 sequences. (Running on oeis4.)