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A108852 Number of Fibonacci numbers <= n. 9
1, 3, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..80.

FORMULA

G.f.: (Sum_{n>=0} x^Fibonacci(n))/(1-x). - Vladeta Jovovic, Nov 27 2005

a(n) = 1+floor(log_phi((sqrt(5)*n+sqrt(5*n^2+4))/2)), n>=0, where phi is the golden ratio. Alternatively, a(n)=1+floor(arcsinh(sqrt(5)*n/2)/log(phi)). Also a(n)=A072649(n)+2. - Hieronymus Fischer, May 02 2007

a(n) = 1+floor(log_phi(sqrt(5)*n+1)), n>=0, where phi is the golden ratio. - Hieronymus Fischer, Jul 02 2007

MATHEMATICA

fibPi[n_] := 1 + Floor[ Log[ GoldenRatio, 1 + n*Sqrt@ 5]]; Array[fibPi, 80, 0] (* Robert G. Wilson v, Aug 03 2014 *)

PROG

(Haskell) fibs :: [Integer]

fibs = 0 : 1 : zipWith (+) fibs (tail fibs)

fibs_to :: Integer -> Integer

fibs_to n = length $ takeWhile (<= n) fibs

CROSSREFS

Cf. A060384, A072649.

Sequence in context: A098200 A092405 A130234 * A179413 A119476 A307136

Adjacent sequences:  A108849 A108850 A108851 * A108853 A108854 A108855

KEYWORD

nonn

AUTHOR

Michael C. Vanier (mvanier(AT)cs.caltech.edu), Nov 27 2005

STATUS

approved

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Last modified December 15 00:30 EST 2019. Contains 329988 sequences. (Running on oeis4.)