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Pierpont primes

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Finesse version

This finesse version never produces more Pierpont numbers than it needs to fulfill the requested number of primes. It uses a series of parallel iterators with additional iterators added as required. No need to speculatively generate an overabundance. No need to rely on magic numbers. No need to sort them. It produces exactly what is needed, in order, on demand.

use ntheory:from<Perl5> <is_prime>;

sub pierpont ($kind is copy = 1) {
    fail "Unknown type: $kind. Must be one of 1 (default) or 2" if $kind !== 1|2;
    $kind = -1 if $kind == 2;
    my $po3 = 3;
    my $add-one = 3;
    my @iterators = [1,2,4,8 … *].iterator, [3,9,27 … *].iterator;
    my @head = @iterators».pull-one;

    gather {
        loop {
            my $key = @head.pairs.min( *.value ).key;
            my $min = @head[$key];
            @head[$key] = @iterators[$key].pull-one;

            take $min + $kind if "{$min + $kind}".&is_prime;

            if $min >= $add-one {
                @iterators.push: ([|((2,4,8).map: * * $po3) … *]).iterator;
                $add-one = @head[+@iterators - 1] = @iterators[+@iterators - 1].pull-one;
                $po3 *= 3;
            }
        }
    }
}

say "First 50 Pierpont primes of the first kind:\n" ~ pierpont[^50].rotor(10)».fmt('%8d').join: "\n";

say "\nFirst 50 Pierpont primes of the second kind:\n" ~ pierpont(2)[^50].rotor(10)».fmt('%8d').join: "\n";

say "\n250th Pierpont prime of the first kind: " ~ pierpont[249];

say "\n250th Pierpont prime of the second kind: " ~ pierpont(2)[249];

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Output:

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Generalized Pierpont iterator

Alternately, a version that will generate generalized Pierpont numbersarrow-up-right for any set of prime integers where at least one of the primes is 2.

(Cut down output as it is exactly the same as the first version for {2,3} +1 and {2,3} -1; leaves room to demo some other options.)

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Output:

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