OFFSET
1,3
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
FORMULA
a(n)=c(n), if (n^2-4)/5 is a square number, a(n)=s(n), if (n^2+4)/5 is a square number and a(n)=floor(log_phi(n)) otherwise, where s(n)=floor(arcsinh(n/2)/log(phi)), c(n)=floor(arccosh(n/2)/log(phi)) and phi=(1+sqrt(5))/2.
a(n) = A130241(n) except for n=2.
G.f.: g(x) = (1/(1-x))*(Sum_{k>=1} x^Lucas(k)) - x^2.
a(n) = floor(log_phi(n+1/2)) for n >= 3, where phi is the golden ratio.
EXAMPLE
a(2)=0, since Lucas(0)=2; a(10)=4, since Lucas(4) = 7 < 10 but Lucas(5) = 11 > 10.
MATHEMATICA
Join[{1, 0}, Table[Floor[Log[GoldenRatio, n + 1/2]], {n, 3, 50}]] (* G. C. Greubel, Dec 21 2017 *)
PROG
(Python)
from itertools import islice, count
def A130247_gen(): # generator of terms
yield from (1, 0)
a, b = 3, 4
for i in count(2):
yield from (i, )*(b-a)
a, b = b, a+b
CROSSREFS
KEYWORD
nonn
AUTHOR
Hieronymus Fischer, May 19 2007, Jul 02 2007
STATUS
approved