The starting point is a result of R.F.C. Walters in Alternate derivation of some regular continued fractions, J. Austr. Math. Soc 8 (1968), 205-212): If
then pn/rn and qn/sn → el/m.
We first find the least n=n* such that pn, qn, rn, sn are non-negative and repeatedly apply Raney's factorisation for n*≤ k ≤ n*+N, as in Davison's example in §3.
The number (count) of partial quotients of el/m found is returned.
We cannot predict the value of count, but it becomes positive for sufficiently large N.
We suggest taking l/m no greater than say 14, because of the time taken to compute a0.
This is a BCMATH translation of a BC program.
A faster C version is available.
Inside the program, l and m are replaced by l/gcd(l,m) and m/gcd(l,m).
Last modified 1st June 2006
Return to main page