This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A080988 #15 Dec 14 2024 14:36:30 %S A080988 1,5,115,57155,13457544835,718532108172999980195, %T A080988 1987460976488531436231264449305834729789315, %U A080988 14835338180729281137836887250133924105479472089418750626398379615457041439472496214755 %N A080988 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 A080988 Suggested by _Leroy Quet_, Feb 26 2003. %F A080988 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 A080988 The sequence begins 1, 5/4, 115/76, 57155/31996, 13457544835/6509938156, ... %t A080988 NestList[#+1/(3+1/#)&,1,10]//Numerator (* _Harvey P. Dale_, Dec 13 2018 *) %o A080988 (Reduce) a := 1; for i := 1:8 do write a := a+1/(3+1/a); %Y A080988 Cf. A080989, A080990, A080991, A079269, A079278. %K A080988 frac,nonn %O A080988 1,2 %A A080988 _Hugo Pfoertner_, Feb 26 2003