I stumbled upon a programming challenge where I needed to find the numbers whose summation of digits raised to the consecutive powers is equal to the number itself. Like for example: $89 = 8 ^ 1 + 9 ^ 2$
and the next in the series is 135
$135 = 1^1+3^2+5^3$
What are these type of numbers known as? Is there any generic test so as to check if the number is of this type?
I'm not much familiar with number theory so please forgive my ignorance.
If there is a similar question asked can someone point me in the right direction.