%I A080984
%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 Suggested by Leroy Quet Feb 26 2003.
%H A080984 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> 
               (listed in lieu of email address)
%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 begins 1, 4/3, 56/33, 9968/4785, 294115808/118289985, ...
%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.
%Y A080984 Sequence in context: A070019 A056075 A000315 this_sequence A071579 A060497 
               A092273
%Y A080984 Adjacent sequences: A080981 A080982 A080983 this_sequence A080985 A080986 
               A080987
%K A080984 frac,nonn
%O A080984 1,2
%A A080984 Hugo Pfoertner (hugo(AT)pfoertner.org), Feb 26 2003