Calculating the simple continued fraction of log_ba

Note that log_ba = 1/log_ab, it suffices to deal with the case a > b.
We run the algorithm for c = b^r, r = m,...,n (suggested by Alan Offer).
Here a, b, m, n are positive integers satisfying a > b > 1, and 1 ≤ m ≤ n.

In version 1, we employ the criterion A_i,c > c + b√c in the main loop and usually correct partial quotients are returned.
However the example (a,b,m,n)=(991,2,146,148) shows that there are exceptions.

In version 2, we use the stronger cutoff condition A_i,c > c + b²√c in the main loop, and this anomaly disappears.
However fewer partial quotients will be returned compared with version 1.

Last modified 8th August 2019
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