login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

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).
2

%I #15 Dec 14 2024 14:36:30

%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