9
A prime knot is:
a non-trivial knot which cannot be written as the knot sum of two non-trivial knots.
Explanation of a knot-sum: put the two knots adjacent,
... then draw two lines between them, to the same strand on each side, and remove the part between the lines you just drew. This composition of two knots will form a new, non-prime knot.
Here are all prime knots with 7 or fewer crossings (the Unknot is not prime):
You need to output the number of unique prime knots for a given number of crossings.
1 0
2 0
3 1
4 1
5 2
6 3
7 7
8 21
9 49
10 165
11 552
12 2176
13 9988
14 46972
15 253293
16 1388705
I don't think the values are known for inputs larger than 16
, but if given such an input, your code would need to find the correct result given enough time.
1
Perhaps someone will find this Mathematica library useful.
– mbomb007 – 2016-12-19T20:44:46.003