Talk:Jacobsthal number

Ford-Johnson merge-insertion sort

In the field of computer sciences, the Jacobsthal numbers appear in the implementation of the Ford-Johnson merge-insertion sort. I couldn't find any mention of the name "Jacobsthal", but Donald Knuth gives the first numbers used by the algorithm in The Art of Computer Programming, Volume 3: $(1,3,5,11,...)$, then gives the formula used to get the following numbers: $t_{k}={\frac {2^{k+1}+(-1)^{k}}{3}}$ which gives a sequence close to Jacobsthal numbers. The only difference is that the sequence doesn't have the leading $0$.

Moreover, Knuth then says that the same sequence appears in an algorithm used to compute the greatest common divisor of 2 integers. Mentioning how Jacobsthal numbers appear in actual algorithms could be an interesting addition to the article. 92.135.149.127 (talk) 10:28, 9 January 2016 (UTC)

Jacobsthall Numbers

I think there's an error on this page where it says the FIRST recurrence relation is satisfied by the powers of 2, I think this is wrong. I think the 2nd recurrence relation, i.e. the one immediately above the comment is the recurrence relation that the powers of 2 satisfy. 213.205.242.85 (talk) 10:02, 15 March 2018 (UTC)