OFFSET
1,2
COMMENTS
A Collatz-Fibonacci mixture. Does this sequence diverge to infinity? [Yes! See Amleh et al. - N. J. A. Sloane, Jun 17 2009]
Conjecture: More generally, let a(1)=x and a(2)=y be two distinct positive integers; then for any x,y > 0, lim n -> infinity log(a(n))/n = 1/4.
LINKS
Ivan Neretin, Table of n, a(n) for n = 1..1000
A. M. Amleh et al., On Some Difference Equations with Eventually Periodic Solutions, J. Math. Anal. Appl., 223 (1998), 196-215. [N. J. A. Sloane, Jun 17 2009]
J. Greene, The Unboundedness of a Family of Difference Equations Over the Integers, Fib. Q., 46/47 (2008/2009), 146-152. [N. J. A. Sloane, Jun 17 2009]
FORMULA
a(n+2) = 2*(a(n+1) + a(n))/(3 + (-1)^(a(n+1) + a(n))).
It seems that a(n)*exp(-n/4) is bounded.
EXAMPLE
a(1)=1 and a(2)=2 have different parities, hence a(3)=a(2)+a(1)=3.
MATHEMATICA
Nest[Append[#, If[OddQ[#], #, #/2] &@(#[[-1]] + #[[-2]])] &, {1, 2}, 47] (* Ivan Neretin, Sep 07 2017 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Apr 11 2002
STATUS
approved