Self obsessed numbers

Computer Science Level 5

Consider a \(n\) digit integer \(x=\overline{a_na_{n-1}\cdots a_1}\).

Let us call the number \(x\) to be self obsessed if

\(x=\overline{a_na_{n-1}\cdots a_1}=a_n^{a_n}+a_{n-1}^{a_{n-1}}+\cdots+a_1^{a_1}\).

It is easy to see that the smallest such integer is \(x=1\).

What is the next integer with this property?

HINT : \(0^0\) is . Hence, the answer cannot have zero as one of its digits.


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