readme.MD

Instal

cd somewhere
composer require brick/math
php index.php

Example

New max len: 2
New result: 11111112222223344444444444444666666666666666666677777

New max len: 3
New result: 333334444444777777

New max len: 4
New result: 1112246699999999

New max len: 5
New result: 1111122222337777

New max len: 6
New result: 3333666666666777

New max len: 7
New result: 11111444447777999

New max len: 8
New result: 1111113333333344444444444499999

New max len: 9
New result: 111166666677777

New max len: 10
New result: 111111222222333333344477

New max len: 11
New result: 44777779999999999

index.php

<?php

use Brick\Math\BigInteger;

require __DIR__.'/vendor/autoload.php';

global $digits;
$digits = [2, 3, 4, 6, 7, 8, 9];

$maxLen = 0;

while (true) {
    $counts = randomCounts();
    $number = buildNumber($counts);
    if ($number === null) {
        continue;
    }

    $len = calcLen($number);

    // Hooray
    if ($len > $maxLen) {
        echo "New max len: $len\n";
        echo "New result: $number\n\n";

        $maxLen = $len;
        continue;
    }
}

/**
 * Get random number of all given digits
 *
 * Sometimes it returns all zeros
 *
 * @return array. Key is digit value is number of repeats
 */
function randomCounts(): array
{
    global $digits;

    $counts = [];
    foreach ($digits as $digit) {
        $rnd = rand(0, 100);

        if ($rnd < 40) {
            $counts[$digit] = 0;
        } elseif ($rnd < 70) {
            $counts[$digit] = rand(1, 5);
        } elseif ($rnd < 90) {
            $counts[$digit] = rand(6, 10);
        } elseif($rnd < 99) {
            $counts[$digit] = rand(11, 15);
        } else {
            $counts[$digit] = rand(16, 25);
        }
    }

    return $counts;
}

/**
 * Builds a number from counts
 *
 * @param array $counts result of the previous function
 *
 * @return BigInteger|null null if all numbers are zeros
 */
function buildNumber(array $counts): ?BigInteger
{
    // The test number from the video
//    return BigInteger::of('277777788888899');

    $num = '';
    foreach ($counts as $digit => $count) {
        $num .= str_repeat($digit, $count);
    }

    if ($num == '') {
        return null;
    }

    return BigInteger::of($num);
}

/**
 * Count the number of steps for the given number
 *
 * @param BigInteger $integer
 *
 * @return int
 */
function calcLen(BigInteger $integer): int
{
    $str = (string)$integer;
    $len = strlen($str);

    if ($len == 1) {
        return 0;
    }

    $multi = BigInteger::of(1);

    for ($i = 0; $i < $len; $i++) {
        $multi = $multi->multipliedBy($str[$i]);
    }

    return calcLen($multi) + 1;
}