A080989 -id:A080989 - cp's OEIS frontend

A080991 Ratios of successive terms of A080989.

4, 19, 421, 203461, 46882572661, 2460798973136286293701, 6713425293781487374296340087251890561890261, 49548081347487610687284649853537701683093220643723475323834248591924587627064854208741

Offset: 1

Hugo Pfoertner, Feb 26 2003

nonn

Cf. A080989, A080582, A080987.

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).

Original entry on oeis.org

1, 5, 115, 57155, 13457544835, 718532108172999980195, 1987460976488531436231264449305834729789315, 14835338180729281137836887250133924105479472089418750626398379615457041439472496214755

Offset: 1

Hugo Pfoertner, Feb 26 2003

Suggested by Leroy Quet, Feb 26 2003.

			The sequence begins 1, 5/4, 115/76, 57155/31996, 13457544835/6509938156, ...

Cf. A080989, A080990, A080991, A079269, A079278.

NestList[#+1/(3+1/#)&,1,10]//Numerator (* Harvey P. Dale, Dec 13 2018 *)

a := 1; for i := 1:8 do write a := a+1/(3+1/a);

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])

cp's OEIS Frontend

A080991 Ratios of successive terms of A080989.

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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).

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