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 A289909 Numerator of r(n), where r(n) = 1/r(n-2) + r(n-1); r(1)=r(2)=1/2. 1
 1, 1, 5, 9, 49, 461, 23489, 11225329, 272637326981, 3157526775628390649, 886457726538825109967312921569, 2877355448368368144942636577290120976530764462381, 2618094955775549169448195139184997935943619201377536713185932400811680633788689 (list; graph; refs; listen; history; text; internal format)
 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 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: A100457 A080872 A173776 * A000324 A123817 A124421 Adjacent sequences:  A289906 A289907 A289908 * A289910 A289911 A289912 KEYWORD nonn,frac AUTHOR John Harmon, Jul 15 2017 STATUS approved

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Last modified October 17 22:48 EDT 2018. Contains 316297 sequences. (Running on oeis4.)