Shouldn't the sequence start with two of the highest values in your memoization container instead of (1,1)?

Frankly, all solutions here I saw but for 54d7ac's one (mathematically optimal, but won't scale to big integers, transformation matrix is better for that, although brings O(log(n)) instead of O(1)) are heavily suboptimal anyway so it depends what you aim for. ;) I aimed for Iterator approach.

Overkill

There is a problem with Nim tests that is difficult to see.
Tests can be green with "Passed etc..." even if some fail.
Look if there is a small orange rectangle near "Tests results", in that case at least one test have failed.
I reported the bug at CW. Please see https://github.com/Codewars/codewars.com/issues/1087.
Complete this bug report by your observation. That could hopefully speed up a fix to that.
Sorry for the inconvenience.

Cheating, it doesn't work for any m >= 200. :-/

My solution in Nim passes all the tests but, oddly, the button doesn't change to Submit Final.

Just like you use div operator, use mod. It's much more natural than unsigned-mod %% operator.

Many thanks for your contribution; reviewed and approved :D

Thanks. By the way, if you have any suggestions to improve Nim support on Codewars, please let me know by opening an issue on Codewars/codewars-runner-cli.

x.toInt does the same as round(x).int but is shorter and (probably) more efficient.

Use a div b for integer division, not int(a / b).

Probably better than my own little obsession, namely: "I know it already passes tests but I can make it better composed/more general/nicer to read". ;)

:D Why do more when you can do the same with less? (Don't answer that...I know the correct answer)

I felt it's a bit un-pytonish to actually add methods to an existing class without no real reason.