Source code in the raku programming language

constant @sq = ^10 X** 2;
my $cnt = 0;

sub Euler92($n) {
    $n == any(1,89) ?? $n !!
    (state %){$n} //= Euler92( [+] @sq[$n.comb] )
}

for 1 .. 1_000_000 -> $n {
   my $i = +$n.comb.sort.join;
   ++$cnt if Euler92($i) == 89;
}
 
say $cnt;


my @cache;
@cache[1] = 1;
@cache[89] = 89;

sub Euler92(int $n) {
    $n < 649  # 99,999,999 sums to 648, so no point remembering more
        ?? (@cache.AT-POS($n) //= ids($n))
        !! ids($n)
}

sub ids(int $num --> int) {
    my int $n = $num;
    my int $ten = 10;
    my int $sum = 0;
    my int $t;
    my int $c;
    repeat until $n == 89 or $n == 1 {
        $sum = 0;
        repeat {
            $t = $n div $ten;
            $c = $n - $t * $ten;
            $sum = $sum + $c * $c;
        } while $n = $t;
        $n = @cache.AT-POS($sum) // $sum;
    }
    $n;
}

my int $cnt = 0;
for 1 .. 100_000_000 -> int $n {
   $cnt = $cnt + 1 if Euler92($n) == 89;
}
say $cnt;


sub endsWithOne($n --> Bool) {
    my $digit;
    my $sum = 0;
    my $nn = $n;
    loop {
        while $nn > 0 {
            $digit = $nn % 10;
            $sum += $digit²;
            $nn = $nn div 10;
        }
        return True  if $sum == 1;
        return False if $sum == 89;
        $nn = $sum;
        $sum = 0;
    }
}

my $k = 8; # 10**8
my @sums is default(0) = 1,0;
my $s;
for 1 .. $k -> $n {
    for $n*81 … 1 -> $i {
        for 1 .. 9 -> $j {
            $s = $j²;
            last if $s > $i;
            @sums[$i] += @sums[$i - $s];
        }
    }
}

my $ends-with-one = sum flat @sums[(1 .. $k*81).grep: { endsWithOne($_) }], +endsWithOne(10**$k);

say 10**$k - $ends-with-one;