%I #20 Jul 15 2017 11:23:14
%S 1,1,5,9,49,461,23489,11225329,272637326981,3157526775628390649,
%T 886457726538825109967312921569,
%U 2877355448368368144942636577290120976530764462381,2618094955775549169448195139184997935943619201377536713185932400811680633788689
%N Numerator of r(n), where r(n) = 1/r(n-2) + r(n-1); r(1)=r(2)=1/2.
%C It appears that the sequence is always in simplest terms when generated.
%C What happens when we generalize this to r(1) = r(2) = a/b?
%F r(n) = a(n)/A289910(n).
%e For n=3 r(3)=1/r(2) + r(1) which is 5/2 = 2/1 + 1/2.
%e For n=4 r(4)= 2/1 + 5/2 = 9/2.
%e For n=5 r(5)= 2/5 + 9/2 = 49/10.
%t r[n_] := r[n] = If[n <= 2, 1/2, 1/r[n - 2] + r[n - 1]]; Numerator@ Array[r, 13] (* _Michael De Vlieger_, Jul 15 2017 *)
%Y Cf. A289910 (denominators).
%K nonn,frac
%O 1,3
%A _John Harmon_, Jul 15 2017