Calculating the simple continued fraction of log(a)/log(b)

Calculating the simple continued fraction of log_ba

This performs an algorithm based on a paper of T.H. Jackson and K.R. Matthews, On Shanks' algorithm for computing the continued fraction of log_ba, Journal of Integer Sequences 5 (2002) article 02.2.7.
Our algorithm is described in the altered version of that paper.

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.
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.
If we use the stronger cutoff condition A_i,c > c + b²√c in the main loop, as in http://www.numbertheory.org/php/log3.html, this anomaly disappears. However fewer partial quotients will be returned.

Last modified 6th January 2019
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Calculating the simple continued fraction of logba

Calculating the simple continued fraction of log_ba