Solutions by Walt Mankowski.

# Perl Weekly Challenge #173: Esthetic Numbers and Sylvester's Sequence

I did this week's challenge in Perl and Python.

## Task #1: Esthetic Numbers

For this task we're given a number _n_ and need to determine if it's an Esthetic Number. An **Esthetic Number** is a positive integer where every pair of adjacent digits differ in value by exactly 1.

The only real trick to solve this in Perl is that we can turn a number `$n` into an array of digits `@d` with the statement `@d = split //, $n;`. Then we can wrap that in a function that checks the absolute value of each pair of points:

```perl
sub is_esthetic($n) {
    my @d = split //, $n;
    for my $i (1..$#d) {
        return 0 unless abs($d[$i-1] - $d[$i]) == 1;
    }
    return 1;
}
```

Python is more of a stickler about types than Perl, so to turn it into an array of digits I had to first turn it into a string. Then you can treat it as an array, and I turned each character back into an integer. That sounds like a lot of work, but it's just a one-liner with a linst comprehension:

```python
d = [int(c) for c in str(n)]
```

## Task 2: Sylvester's Sequence

For this task we need to generate the first 10 terms of [Sylvester's Sequence](https://en.wikipedia.org/wiki/Sylvester%27s_sequence). **Sylvester's Sequence** is an integer sequence where every term is the product of all the previous terms, plus one.

Terms in Sylvester's Sequence get very large very fast (the 10th term has 20 digits) so we need to use the `bigint` module. I also used the `prod` function from `List::Util` to do the multiplication. With those modules in hand, we can solve this challenge in just a few lines of code:

```perl
use bigint;
use List::Util qw(product);

my @sylvester;
push @sylvester, 1 + product @sylvester while @sylvester < 10;
say for @sylvester;
```

Python has the equivalent of `bigint` built-in, so I didn't need to do anything special there. Python has `sum` as a built-in function but it doesn't have `prod`. There are a few different ways to do write it; I chose to use the `reduce` function from the `functools` package:

```python
def product(lst):
    return reduce(lambda x,y: x*y, lst, 1)
```

But it's so short that I decided to just write it inline. Here's my full program:

```python
from functools import reduce

sylvester = []
while len(sylvester) < 10:
    sylvester.append(reduce(lambda x,y: x*y, sylvester, 1) + 1)

for syl in sylvester:
    print(syl)
```