Geodesic
On Shanks' algorithm for computing the continued fraction of $\log_b a$
Journal of integer sequences, Tome 5 (2002) no. 2.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     author = {Jackson, Terence and Matthews, Keith},
     title = {On {Shanks'} algorithm for computing the continued fraction of $\log_b a$},
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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/