Calculating the simple continued fraction of logba
This performs an algorithm from T.H. Jackson and K.R. Matthews, On Shanks' algorithm for computing the continued fraction of logba, Journal of Integer Sequences 5 (2002) article 02.2.7.
We run the algorithm for c = dr, r = m,...,n.
Here a, b, d, m, n are positive integers satisfying a > b > 1, d > 1 and 1 ≤ m ≤ n.
With d=b, we have found that apart from a few initial exceptional values of r, the correct partial quotients will be returned.
Moreover, with d = b and a = b + 1, it seems that the correct partial quotients are always returned.
This is a BCMath version of the BC program log
- (a,b,d,m,n)=(3730,371,371,1,30) is spectacularly incorrect on line 11, but otherwise seems to be well behaved.
- (a,b,d,m,n)=(2741,4,4,1,30) is incorrect on lines 10 and 15.
- (a,b,d,m,n)=(3,2,2,1,30) is well behaved.
- (991,2,2,1,n) seems to be correct if n > 146.
Last modified 21st March 2018
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