Raku challenge Week 3

In this post, there’re my solutions to the tasks of Week 3 of the Perl Weekly Challenge.

Task 1

Generate a list of Regular numbers, which are the numbers, whose prime factors do not exceed 5.

In my book Using Raku, there is an example of computing prime factors of a number. Actually, that solution can be simplified to the following code, as we don’t need to keep track of repeated factors:

my $max = 20;
my @prime = grep *.is-prime, ^$max;

for 1..$max -> $n {
    say "Prime factor(s) of $n: " ~ grep {$n %% $_}, @prime;
}

For the numbers below 20, we have the following result:

$ raku prime-factors.raku 
Prime factor(s) of 1: 
Prime factor(s) of 2: 2
Prime factor(s) of 3: 3
Prime factor(s) of 4: 2
Prime factor(s) of 5: 5
Prime factor(s) of 6: 2 3
Prime factor(s) of 7: 7
Prime factor(s) of 8: 2
Prime factor(s) of 9: 3
Prime factor(s) of 10: 2 5
Prime factor(s) of 11: 11
Prime factor(s) of 12: 2 3
Prime factor(s) of 13: 13
Prime factor(s) of 14: 2 7
Prime factor(s) of 15: 3 5
Prime factor(s) of 16: 2
Prime factor(s) of 17: 17
Prime factor(s) of 18: 2 3
Prime factor(s) of 19: 19
Prime factor(s) of 20: 2 5

Now let’s use this program as a base for solving the task. If the number is Regular, then all of its prime factors are below and including 5, which you can express as:

all(map * <= 5, grep {$n %% $_}, @prime)

Finally, assemble the pieces together:

my $max = 60;
my @prime = grep *.is-prime, ^$max;

for 1..$max -> $n {
    say $n if all(map * <= 5, grep {$n %% $_}, @prime);
}

You get these numbers in the output:

2
3
4
5
6
8
9
10
12
15
16
18
20
24
25
27
30
32
36
40
45
48
50
54
60

Run the program with different maximum values and compare the result with the sequence listed at oeis.org/A051037.

Task 2

Print the Pascal triangle with the given number of rows.

This task is directly solved in the same book, please find a solution on my site.

Let me add some code to print the triangle as a symmetrical shape:

my $rows = 10;

my @row = 1;
my @lines = gather {
    take 1;
    for 1 ..^ $rows {
        @row = (|@row, 0) >>+<< (0, |@row);
        take @row.join(' ');
    }
}

my $width = @lines[*-1].chars;
.say for map({(' ' x ($width - $_.chars) / 2) ~ $_}, @lines);

This is the result for the requested 10 rows:

$ raku ch-2.raku 
             1
            1 1
           1 2 1
          1 3 3 1
         1 4 6 4 1
       1 5 10 10 5 1
     1 6 15 20 15 6 1
    1 7 21 35 35 21 7 1
  1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1

Find the source files of today’s solutions at my GitHub repository.

→ GitHub repository
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