A289909 Numerator of r(n), where r(n) = 1/r(n-2) + r(n-1); r(1)=r(2)=1/2.

1, 1, 5, 9, 49, 461, 23489, 11225329, 272637326981, 3157526775628390649, 886457726538825109967312921569, 2877355448368368144942636577290120976530764462381, 2618094955775549169448195139184997935943619201377536713185932400811680633788689

Offset

1,3

Comments

It appears that the sequence is always in simplest terms when generated.

What happens when we generalize this to r(1) = r(2) = a/b?

Links

Table of n, a(n) for n=1..13.

Formula

r(n) = a(n)/A289910(n).

Example

For n=3 r(3)=1/r(2) + r(1) which is 5/2 = 2/1 + 1/2.
For n=4 r(4)= 2/1 + 5/2 = 9/2.
For n=5 r(5)= 2/5 + 9/2 = 49/10.

Mathematica

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 *)

Crossrefs

Cf. A289910 (denominators).

Sequence in context: A080872 A328333 A173776 * A000324 A123817 A369155

Adjacent sequences: A289906 A289907 A289908 * A289910 A289911 A289912

Keyword

nonn,frac

Author

John Harmon, Jul 15 2017

Status

approved