# Squaring is Daring (1)

The following sequences go by the rule:

$$a_{n+1}$$ = The sum of the squares of the individual digits of $$a_{n}$$

For example, 56 becomes 61, because $$5^{2}$$ + $$6^{2}$$ = $$25 + 36$$ = 61.

The following is an example of a bad sequence, because it reaches the number 1, and stays there.

{28, 68, 100, 1, 1, 1…}

The following is an example of a good sequence, because it repeats and is non-terminating:

{30, 3, 9, 81, 65, 61, 37, 58, 89, 145, 42, 20, 2, 4, 16, 37…}

If I create all sequences from 51 to 60 (inclusive), how many will be "good"?

Super Challenge: Can you find the general set of starting numbers that will make a sequence "good"/"bad"?

Ultimate Challenge: Prove It!

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