# Self obsessed numbers

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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