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.
Remove the small words from a list of words.
Vectorize the digits of an Integer
Permute diagonal and antidiagonal
Area of an equilateral triangle
Find a Pythagorean triple
Find all vampire fangs
Fangs of a vampire number
Multivariate polynomials - convert monomial form to array
Multivariate polynomials - emulate symbolic form
Negation the hard way
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