OFFSET
1,1
COMMENTS
This sequence is infinite if and only if b(n) does not equal -b(n+1) for every positive integer n.
LINKS
Jinyuan Wang, Table of n, a(n) for n = 1..18
FORMULA
For n >= 5, b(n) = - (b(n-1) + b(n-2)) * (b(n-2) + b(n-3)) / (b(n-1) * b(n-2)^2).
EXAMPLE
{b(k)} begins: 2, -2/3, 3, 7/3, -16/27, 141/49, -3023/768, ...
So for example, 1/2 - 3/2 + 1/3 = 2 + 1/(-2/3 + 1/(3 + 3/7)) and 1/2 - 3/2 + 1/3 + 3/7 = 2 + 1/(-2/3 + 1/(3 + 1/(7/3 - 27/16))).
PROG
(PARI) lista(nn) = my(w, x=-2/3, y=3, z=7/3); print1("2, -2, 3, 7"); for(n=5, nn, print1(", ", numerator(w=-(y+z)*(x+y)/y^2/z)); x=y; y=z; z=w); \\ Jinyuan Wang, Aug 09 2021
CROSSREFS
KEYWORD
sign,frac
AUTHOR
Leroy Quet, Mar 27 2007
EXTENSIONS
More terms from Jinyuan Wang, Aug 09 2021
STATUS
approved