A Disarium number is an integer where the sum of each digit raised to the power of its position in the number, is equal to the number.



E.G.
135 is a Disarium number:

 11 + 32 + 53 == 1 + 9 + 125 == 135

There are a finite number of Disarium numbers.



Task
 Find and display the first 18 Disarium numbers.


Stretch
 Find and display all 20 Disarium numbers.


See also
 Geeks for Geeks - Disarium numbers
 OEIS:A032799 - Numbers n such that n equals the sum of its digits raised to the consecutive powers (1,2,3,...)
 Related task: Narcissistic decimal number
 Related task: Own digits power sum Which seems to be the same task as Narcissistic decimal number...




module Disarium 
   where
import Data.Char ( digitToInt)
 
isDisarium :: Int -> Bool
isDisarium n = (sum $ map (\(c , i ) -> (digitToInt c ) ^ i )
 $ zip ( show n ) [1 , 2 ..]) == n
 
solution :: [Int]
solution = take 18 $ filter isDisarium [0, 1 ..]
 