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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). 10
 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 G. C. Greubel, Table of n, a(n) for n = 0..10000 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^Fibonacci(2*k). 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. MATHEMATICA Table[Floor[1/2*Log[GoldenRatio, (Sqrt[5]*n + 1)]], {n, 0, 100}] (* G. C. Greubel, Sep 12 2018 *) PROG (PARI) vector(100, n, n--; floor(log((sqrt(5)*n+1))/(2*log((1+sqrt(5))/2) ))) \\ G. C. Greubel, Sep 12 2018 (MAGMA) [Floor(Log((Sqrt(5)*n+1))/(2*Log((1+Sqrt(5))/2)))): n in [0..100]]; // G. C. Greubel, Sep 12 2018 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 January 23 10:48 EST 2020. Contains 331171 sequences. (Running on oeis4.)