Brainteaser 1712: Squambling

From The Sunday Times, 9th July 1995 [link]

In “squambling” a number, the first (leftmost) digit is squared, the next is cubed, the next raised to the fourth power, and so on. The total of these answers provides a new number, ready for the squambling to begin again.

For example:

18 → 1² + 8³ = 513 → 5² + 1³ + 3⁴ = 107
107 → 2402 → 100 → 1 → 1 → …

If you take my age and squamble it you get a three-figure number. If you then squamble that answer you get my age next year.

How old am I?

This puzzle was included in the book Brainteasers (2002, edited by Victor Bryant). The puzzle text above is taken from the book.

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