Brazilian numbers

Brazilian numbers are so called as they were first formally presented at the 1994 math Olympiad Olimpiada Iberoamericana de Matematica in Fortaleza, Brazil.

Brazilian numbers are defined as:

The set of positive integer numbers where each number N has at least one natural number B where 1 < B < N-1 and where the representation of N in base B has all equal digits.

E.G.

1, 2 & 3 can not be Brazilian; there is no base B that satisfies the condition 1 < B < N-1.
4 is not Brazilian; 4 in base 2 is 100. The digits are not all the same.
5 is not Brazilian; 5 in base 2 is 101, in base 3 is 12. There is no representation where the digits are the same.
6 is not Brazilian; 6 in base 2 is 110, in base 3 is 20, in base 4 is 12. There is no representation where the digits are the same.
7 is Brazilian; 7 in base 2 is 111. There is at least one representation where the digits are all the same.
8 is Brazilian; 8 in base 3 is 22. There is at least one representation where the digits are all the same.
and so on...

All even integers 2P >= 8 are Brazilian because 2P = 2(P-1) + 2, which is 22 in base P-1 when P-1 > 2. That becomes true when P >= 4.

Task

Write a routine (function, whatever) to determine if a number is Brazilian and use the routine to show here, on this page;

the first 20 Brazilian numbers;
the first 20 odd Brazilian numbers;
the first 20 prime Brazilian numbers;

See also

Perl 6

Works with: Rakudo version 2019.07.1

<lang perl6>sub is-Brazilian (Int $n) {

   for 2 ..^ $n - 1 { return True if +(my @b = $n.polymod( $_ xx * )) > 1 and [==] @b }
   False

}

my @Brazilians = lazy (^Inf).hyper.grep: { .&is-Brazilian }

put "First 20 Brazilian numbers:\n", @Brazilians[^20];

put "\nFirst 20 odd Brazilian numbers:\n", @Brazilians.grep( * % 2 )[^20];

put "\nFirst 20 prime Brazilian numbers:\n", @Brazilians.grep( *.is-prime )[^20];</lang>

Output:

First 20 Brazilian numbers:
7 8 10 12 13 14 15 16 18 20 21 22 24 26 27 28 30 31 32 33

First 20 odd Brazilian numbers:
7 13 15 21 27 31 33 35 39 43 45 51 55 57 63 65 69 73 75 77

First 20 prime Brazilian numbers:
7 13 31 43 73 127 157 211 241 307 421 463 601 757 1093 1123 1483 1723 2551 2801