OFFSET
0,5
FORMULA
Also the rounded values of the sequence of real numbers g(n) defined by g(0) = 0, g(1) = 1, then g(n) = (g(n-1)^2 + g(n-2)^2)^(1/2). - Corrected by Thomas Ordowski, Jan 05 2013
This is a special case of the following conjectured relationship: Given a starting sequence of g(0)=0, g(1)=1, ..., g(m)=1 (i.e., 0 then m-1 1's) and then a recurrence relation g(n) = b_1*g(n-1)^c_1 + b_2*g(n-2)^c_2 + ... + b_m*g(n-m)^c_m where the b_i's and c_i's are real numbers > 0 then (b_1*(g(n-1)^c_1)^x + b_2*(g(n-2)^c_2)^x + ... + b_m*(g(n-m)^c_m)^x)^(1/x) = g(n)^(1/x) where x is a real number > 0. - Gerald McGarvey, Dec 12 2004
MATHEMATICA
Table[ Round[ Sqrt[ Fibonacci[ n]]], {n, 0, 50}] (* Robert G. Wilson v Dec 10 2004 *)
PROG
(Python)
from gmpy2 import isqrt, fib
def A100665(n): return int((m:=isqrt(k:=fib(n)))+(k-m*(m+1)>=1)) # Chai Wah Wu, Jun 19 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Gerald McGarvey, Dec 04 2004
EXTENSIONS
More terms from Robert G. Wilson v, Dec 10 2004
STATUS
approved