Geodesic
On Shanks' algorithm for computing the continued fraction of \(\log_b a\)
Journal of integer sequences, Tome 5 (2002) no. 2
We give a more practical variant of Shanks' 1954 algorithm for computing the continued fraction of log_b $a$, for integers $a > b > 1$, using the floor and ceiling functions and an integer parameter $c > 1$. The variant, when repeated for a few values of $c = 10$^r, enables one to guess if log_b $a$ is rational and to find approximately $r$ partial quotients.
Classification : 11D09
Keywords: shanks' algorithm, continued fraction, log, heuristic algorithm (Concerned with sequence 
@article{JIS_2002__5_2_a6,
     author = {Jackson,  Terence and Matthews,  Keith},
     title = {On {Shanks'} algorithm for computing the continued fraction of \(\log_b a\)},
     journal = {Journal of integer sequences},
     year = {2002},
     volume = {5},
     number = {2},
     zbl = {1020.11083},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2002__5_2_a6/}
}
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Jackson,  Terence; Matthews,  Keith. On Shanks' algorithm for computing the continued fraction of \(\log_b a\). Journal of integer sequences, Tome 5 (2002) no. 2. http://geodesic.mathdoc.fr/item/JIS_2002__5_2_a6/