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Kaprekar n.  and  modest n.

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(max 15 digits)

First numbers that belong to both sets:

999, 7777, 9999, 22222, 99999, 818181, 999999, 4444444, 9999999, 25252525, 36363636, 88888888, 99999999, 432432432, 909090909, 999999999, 1111111111.