## Digit power sum

### Problem 119

Published on Friday, 7th April 2006, 06:00 pm; Solved by 7887; Difficulty rating: 30%The number 512 is interesting because it is equal to the sum of its digits raised to some power: 5 + 1 + 2 = 8, and 8^{3} = 512. Another example of a number with this property is 614656 = 28^{4}.

We shall define *a*_{n} to be the *n*th term of this sequence and insist that a number must contain at least two digits to have a sum.

You are given that *a*_{2} = 512 and *a*_{10} = 614656.

Find *a*_{30}.