Are you sure about the first rule? It doesn't seem necessary according to https://oeis.org/A014575.
The problem is really fun.
Since I created the problem series and want the Functions I badge, I thought I'd provide the solution that incorporates vampire_factor and are_fangs. Not a great score, but readable!
Sorry, I mean the Magic Numbers badge.
Swap the first and last columns
Flip the main diagonal of a matrix
Replace multiples of 5 with NaN
Create an n-by-n null matrix and fill with ones certain positions
Negation the hard way
Multivariate polynomials - convert monomial form to array
Find all vampire fangs
Product of two multivariate polynomials
Multivariate polynomials - sort monomials
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