OFFSET
0,2
COMMENTS
1 is counted twice as a Fibonacci number: F(1) = F(2) = 1. - Alois P. Heinz, Nov 04 2024
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..10000
Dorin Andrica, Ovidiu Bagdasar, and George Cătălin Tųrcąs, On some new results for the generalised Lucas sequences, An. Şt. Univ. Ovidius Constanţa (Romania, 2021) Vol. 29, No. 1, 17-36.
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
MAPLE
a:= proc(n) option remember; `if`(n<2, 2*n+1, a(n-1)+
(t-> `if`(issqr(t+4) or issqr(t-4), 1, 0))(5*n^2))
end:
seq(a(n), n=0..100); # Alois P. Heinz, Nov 04 2024
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
(Python)
def A108852(n):
a, b, c = 0, 1, 0
while a <= n:
a, b = b, a+b
c += 1
return c # Chai Wah Wu, Nov 04 2024
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Michael C. Vanier (mvanier(AT)cs.caltech.edu), Nov 27 2005
STATUS
approved