Kata

A Vampire number is a positive integer z with a factorization x * y = z such that

• x and y have the same number of digits and
• the multiset of digits of z is equal to the multiset of digits of x and y.
• Additionally, to avoid trivialities, x and y may not both end with 0.

In this case, x and y are called fangs of z. (The fangs of a Vampire number may not be unique, but this shouldn't bother us.) The first three Vampire numbers are

1260 = 21*60
1395 = 15*93
1435 = 35*41

Write an algorithm that on input k returns the kth Vampire number. To avoid time-outs, the Python version will test with 1 <= k <= 155.

PS: In the OEIS, the Vampire numbers are sequence A014575.

PPS: So called Pseudo-Vampire Numbers are treated in this kata.