13

Look at them like this: Further explanation:


7

The kinda-famous tells us that where and therefore So


7

The answer is The starting number:


4

Original Answer: Edit: Going in the other direction as suggested in the comment, we notice that: 9056 / 2 = 4528 528 / 2 = 264 So the pattern could also be dividing by 2 and removing the leading digit. Using this approach we get


2

Partial Answer Here are some things I've noticed which might lead somebody else to the answer


2

Allowing for inefficiency in the descriptions of digits, here are 12 digit sequences that describe themselves and cannot be decomposed into smaller solutions. Allowing for infinitely long periodically repeating sequences as well, here are 8 trivial indecomposable periodically repeating infinite solutions until more interesting ones crop up. All of these ...


2

via polynomial interpolation


1

The answer is: You might think I have made a mistake there, but I suggest that you: Try it yourself and see!


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