cp's OEIS Frontend

A080984 Define b by b(1) = 1 and for n > 1, b(n) = b(n-1) + 1/(2 + 1/b(n-1)); sequence gives numerator of b(n).

%I A080984 #19 Dec 23 2024 14:53:42
%S A080984 1,4,56,9968,294115808,242590126064151488,
%T A080984 158248601344912132157178428071499648,
%U A080984 65129411362626329768830076910903417752818896343320137665280356705971968
%N A080984 Define b by b(1) = 1 and for n > 1, b(n) = b(n-1) + 1/(2 + 1/b(n-1)); sequence gives numerator of b(n).
%C A080984 The next term has 285 digits. - _Harvey P. Dale_, Jul 07 2011
%H A080984 Leroy Quet, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/pipermail/seqfan/2003-February/002229.html">Sequence & Its Numerators & Denominators</a>, posting to SeqFan mailing list, Feb 26 2003.
%F A080984 b(k) = n(k)/d(k); n(1)=1, d(1)=1, m=2; for k >= 2: n(k+1) = n(k) *(m*n(k) + 2*d(k)), d(k+1) = d(k)*(m*n(k) + d(k)). - _Leroy Quet_
%e A080984 The sequence {b(n)} begins 1, 4/3, 56/33, 9968/4785, 294115808/118289985, ...
%t A080984 Numerator/@NestList[#+1/(2+1/#)&,1,9] (* _Harvey P. Dale_, Jul 07 2011 *)
%o A080984 (Reduce) a := 1; for i := 1:8 do write a := a+1/(2+1/a);
%Y A080984 Cf. A080985, A080986, A080987, A079269, A079278.
%K A080984 frac,nonn
%O A080984 1,2
%A A080984 _Hugo Pfoertner_, Feb 26 2003