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%I #15 Oct 14 2023 23:43:32
%S 1,4,56,9968,294115808,242590126064151488,
%T 158248601344912132157178428071499648,
%U 65129411362626329768830076910903417752818896343320137665280356705971968
%N 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 Suggested by _Leroy Quet_, Feb 26 2003
%C The next term has 285 digits. - _Harvey P. Dale_, Jul 07 2011
%F 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 The sequence {b(n)} begins 1, 4/3, 56/33, 9968/4785, 294115808/118289985, ...
%t Numerator/@NestList[#+1/(2+1/#)&,1,9] (* _Harvey P. Dale_, Jul 07 2011 *)
%o Reduce: a := 1; for i := 1:8 do write a := a+1/(2+1/a);
%Y Cf. A080985, A080986, A080987, A079269, A079278.
%K frac,nonn
%O 1,2
%A _Hugo Pfoertner_, Feb 26 2003
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