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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). 9
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; text; 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.

LINKS

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

FORMULA

a(n)=floor(arcsinh(sqrt(5)*n/2)/(2*log(phi))), where phi=(1+sqrt(5))/2.

a(n)=A130260(n+1)-1.

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

a(n)=floor(1/2*log_phi(sqrt(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, May 25 2007, Jul 02 2007

STATUS

approved

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Last modified February 18 13:07 EST 2018. Contains 299322 sequences. (Running on oeis4.)