login
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).
2
1, 5, 115, 57155, 13457544835, 718532108172999980195, 1987460976488531436231264449305834729789315, 14835338180729281137836887250133924105479472089418750626398379615457041439472496214755
OFFSET
1,2
COMMENTS
Suggested by Leroy Quet, Feb 26 2003.
FORMULA
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])
EXAMPLE
The sequence begins 1, 5/4, 115/76, 57155/31996, 13457544835/6509938156, ...
MATHEMATICA
NestList[#+1/(3+1/#)&, 1, 10]//Numerator (* Harvey P. Dale, Dec 13 2018 *)
PROG
Reduce: a := 1; for i := 1:8 do write a := a+1/(3+1/a);
CROSSREFS
KEYWORD
frac,nonn
AUTHOR
Hugo Pfoertner, Feb 26 2003
STATUS
approved