%I A108852
%S A108852 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,
%T A108852 10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,
%U A108852 11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11
%N A108852 Number of Fibonacci numbers <= n.
%F A108852 G.f.: (Sum_{n>=0} x^Fibonacci(n))/(1-x). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Nov 27 2005
%F A108852 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
%F A108852 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
%o A108852 (Haskell) fibs :: [Integer]
%o A108852 fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
%o A108852 fibs_to :: Integer -> Integer
%o A108852 fibs_to n = length $ takeWhile (<= n) fibs
%Y A108852 Cf. A060384, A072649.
%Y A108852 Sequence in context: A098200 A092405 A130234 this_sequence A119476 A037038 
               A106501
%Y A108852 Adjacent sequences: A108849 A108850 A108851 this_sequence A108853 A108854 
               A108855
%K A108852 nonn
%O A108852 0,2
%A A108852 Michael C. Vanier (mvanier(AT)cs.caltech.edu), Nov 27 2005