A080990 -id:A080990 - cp's OEIS frontend

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).

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])

A080989 Define b by b(1) = 1 and for n>1, b(n) = b(n-1)+1/(3+1/b(n-1)); sequence gives denominator of b(n).

Original entry on oeis.org

1, 4, 76, 31996, 6509938156, 305202648617286353116, 751042364315893065602546739334386372522316, 5042066805299767273773988103135929366654804375467223444639109745553463308647365564476

Offset: 1

Hugo Pfoertner, Feb 26 2003

Suggested by Leroy Quet, Feb 26 2003.

			See under A080988.

Cf. A080988, A080990, A080991, A079269, A079278.

NestList[#+1/(3+1/#)&,1,10]//Denominator (* Harvey P. Dale, Apr 19 2023 *)

See under A080988.

cp's OEIS Frontend

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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