Blogging back, for the eighth Perl weekly challenge.

This week our two challenges were to calculate the first 5 perfect numbers, and to centre a series of lines on the page.

Perfect Numbers

I’m a little late to the blog this week, so I’ve had a look at what other people did before writing this up (I did my solution before checking out others’), and it looks like a number of people tried to filter the list of positive integers directly. As they discovered, this is mostly fine for the first four perfect numbers, but the fifth… takes a while to discover this way. I didn’t run into this timing issue, because I like to generate.

How do generate perfect number?

The first step is to find an algorithm. This is pretty well documented on the Wikipedia page:

Euclid proved that all numbers of the form q(q + 1) / 2 are perfect numbers where q is (what would later be known as) a Mersenne Prime.

Much more recently, Euler proved that in fact all perfect numbers are formed like this.

So the answer then is to generate Mersenne primes, and calculate perfect numbers using these.

Lazily we Mersenne

A Mersenne prime is of the form 2p - 1 where p is a prime number. So we lazily gather a list of all prime numbers up to ∞, check if they’re prime, apply the formula, and then check if the result is prime as well, because the sequence can produce composite numbers, but Mersenne numbers / primes are always prime.

I bound this to the term M :

my \ M : = ( ^ ∞ ) . grep ( *. is - prime ) . map ( -> $n { 2 ** $n - 1 }) . grep ( *. is - prime );

Perfect Map

The next step is to bind a mapping of the Mersenne primes to the corresponding perfect number:

my \ P : = M . map : -> $q { $q * ( $q + 1 ) div 2 };

I used div so the result is Int not Rat .

Finally, get the results

P is now a lazily generated array that will find the nth Perfect number as P[n] . ^5 gives a list of the first 5, so

P [ ^ 5 ] » . put

Gets the first 5 perfect numbers, then prints each one on its own line.

Text centring

Nothing special here. Like most other people, I found the maximum line length, then padded the average of this and the line length on the left. Only things I did different from what I can see:

Used sprintf. The %*s format specifier lets me pass in the amount of padding without interpolation.

format specifier lets me pass in the amount of padding without interpolation. Filtered through .trim to get rid of any surrounding spaces, because paranoia.

Optional API challenge