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A108852
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Number of Fibonacci numbers <= n.
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8
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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; internal format)
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OFFSET
| 0,2
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FORMULA
| G.f.: (Sum_{n>=0} x^Fibonacci(n))/(1-x). - Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 27 2005
a(n)=1+floor(log_phi((sqr(5)*n+sqr(5*n^2+4))/2)), n>=0, where phi is the golden ratio. Alternatively, a(n)=1+floor(arsinh(sqr(5)*n/2)/ln(phi)). Also a(n)=A072649(n)+2. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 02 2007
a(n)=1+floor(log_phi(sqr(5)*n+1)), n>=0, where phi is the = golden ratio. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jul 02 2007
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PROG
| (Haskell) fibs :: [Integer]
fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
fibs_to :: Integer -> Integer
fibs_to n = length $ takeWhile (<= n) fibs
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CROSSREFS
| Cf. A060384, A072649.
Sequence in context: A098200 A092405 A130234 * A179413 A119476 A037038
Adjacent sequences: A108849 A108850 A108851 * A108853 A108854 A108855
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KEYWORD
| nonn
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AUTHOR
| Michael C. Vanier (mvanier(AT)cs.caltech.edu), Nov 27 2005
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