Problem Statement

An ultra-useful prime is a member of the sequence where each a(n) is the smallest positive integer k such that 2(2n) - k is prime. k must always be an odd number since 2 to any power is always even.

Let's start with the solution:

sub useful ($n) {
    (|$n).map: {
        my $p = 1 +< ( 1 +< $_ );
        ^$p .first: ($p - *).is-prime
    }
}

put useful 1..10;

put useful 11..13;