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%I #11 Dec 13 2018 19:34:13
%S 1,5,115,57155,13457544835,718532108172999980195,
%T 1987460976488531436231264449305834729789315,
%U 14835338180729281137836887250133924105479472089418750626398379615457041439472496214755
%N Define b by b(1) = 1 and for n>1, b(n) = b(n-1)+1/(3+1/b(n-1)); sequence gives numerator of b(n).
%C Suggested by _Leroy Quet_, Feb 26 2003.
%F b[k]=n[k]/d[k]; n[1]=1, d[1]=1, m=3; for k>=2: n[k+1] = n[k] *(m*n[k] + 2*d[k]), d[k+1] = d[k] *(m*n[k] + d[k])
%e The sequence begins 1, 5/4, 115/76, 57155/31996, 13457544835/6509938156, ...
%t NestList[#+1/(3+1/#)&,1,10]//Numerator (* _Harvey P. Dale_, Dec 13 2018 *)
%o Reduce: a := 1; for i := 1:8 do write a := a+1/(3+1/a);
%Y Cf. A080989, A080990, A080991, A079269, A079278.
%K frac,nonn
%O 1,2
%A _Hugo Pfoertner_, Feb 26 2003
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