Problem Statement

A Curzon number is defined to be a positive integer n for which 2n + 1 is evenly divisible by 2 × n + 1. Generalized Curzon numbers are those where the positive integer n, using a base integer k, satisfy the condition that kn + 1 is evenly divisible by k × n + 1. Base here does not imply the radix of the counting system; rather the integer the equation is based on. All calculations should be done in base 10. Generalized Curzon numbers only exist for even base integers.

and even though it is not specifically mentioned that they are Curzon numbers:

Let's start with the solution:

sub curzon ($base) { lazy (1..∞).hyper.map: { $_ if (exp($_, $base) + 1) %% ($base × $_ + 1) } };

for <2 4 6 8 10> {
    my $curzon = .&curzon;
    say "\nFirst 50 Curzon numbers using a base of $_:\n" ~
      $curzon[^50].batch(10)».fmt("%4s").join("\n") ~
      "\nOne thousandth: " ~ $curzon[999]
}