# The Resilience of Magic Numbers

I present to you a magic function that collapses most integers:

Let's take a positive number x, reverse its digits to get y, and get the absolute value of the difference between these two numbers.

After repeating this operation sufficiently many times, most numbers will become 0.

Example x=152, y=251:

**Step 1.** 152 - 251 = -99;

**Step 2.** 99 - 99 = 0.

Though some numbers (like 1012) get stuck in an infinite loop:

1012 -> 1089 -> 8712 -> 6534 -> 2178 -> 6534 -> 2178 -> 6534 ...

There is a list of magic numbers that can not be collapsed by this algorithm:

1012

1023

1034

1045

1056

...

Delving deeper into the world of magic number 1012, it's worth exploring the symbolic significance associated with it. 1012 carries meaning and symbolism that extends beyond the realm of mathematics.

Number 1012 signifies the presence of guardian angels offering guidance and support. Breaking down its digits, 1 represents new beginnings and ambition, 0 symbolizes infinity and spiritual freedom, and 2 embodies diplomacy and balance. The number suggests positive transformations, encouraging personal growth, wisdom, and sensitivity. In matters of love, it emphasizes self-love and avoiding negative influences. Regular sightings of 1012 prompt an optimistic approach to life, positive changes, and a new beginning, guided by the support of guardian angels.

## Non-Zero Converging

Below is a Python returning the first 10 numbers that do not converge to 0 according to the iterative digit reversal rule:def iterative_digit_reversal(num): seen_numbers = set() sequence = [num] while num != 0: reversed_num = int(str(num)[::-1]) num = abs(num - reversed_num) if num in seen_numbers: return sequence, False seen_numbers.add(num) sequence.append(num) return sequence, True def find_first_n_non_zero_converging_numbers(n): non_zero_converging_numbers = [] num = 1 while len(non_zero_converging_numbers) < n: _, converges_to_zero = iterative_digit_reversal(num) if not converges_to_zero: non_zero_converging_numbers.append(num) num += 1 return non_zero_converging_numbers if __name__ == "__main__": first_10_non_zero_converging_numbers = find_first_n_non_zero_converging_numbers(10) print("First 10 Numbers Not Reduced to 0:", first_10_non_zero_converging_numbers)