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...




USING: io kernel lists lists.lazy math.ranges math.text.utils
math.vectors prettyprint sequences ;
 
: disarium? ( n -- ? )
    dup 1 digit-groups dup length 1 [a,b] v^ sum = ;
 
: disarium ( -- list ) 0 lfrom [ disarium? ] lfilter ;
 
19 disarium ltake [ pprint bl ] leach nl