cp's OEIS Frontend

A080989 Define b by b(1) = 1 and for n>1, b(n) = b(n-1)+1/(3+1/b(n-1)); sequence gives denominator of b(n).

%I A080989 #10 Apr 19 2023 13:27:00
%S A080989 1,4,76,31996,6509938156,305202648617286353116,
%T A080989 751042364315893065602546739334386372522316,
%U A080989 5042066805299767273773988103135929366654804375467223444639109745553463308647365564476
%N A080989 Define b by b(1) = 1 and for n>1, b(n) = b(n-1)+1/(3+1/b(n-1)); sequence gives denominator of b(n).
%C A080989 Suggested by _Leroy Quet_, Feb 26 2003.
%F A080989 See under A080988.
%e A080989 See under A080988.
%t A080989 NestList[#+1/(3+1/#)&,1,10]//Denominator (* _Harvey P. Dale_, Apr 19 2023 *)
%o A080989 Reduce: See under A080988.
%Y A080989 Cf. A080988, A080990, A080991, A079269, A079278.
%K A080989 frac,nonn
%O A080989 1,2
%A A080989 _Hugo Pfoertner_, Feb 26 2003