Problem Statement

A positive integer is a Kaprekar number if: Note that a split resulting in a part consisting purely of 0s is not valid, as 0 is not considered positive.

10000 (1002) splitting from left to right:

Generate and show all Kaprekar numbers less than 10,000.

Optionally, count (and report the count of) how many Kaprekar numbers are less than 1,000,000.

The concept of Kaprekar numbers is not limited to base 10 (i.e. decimal numbers); if you can, show that Kaprekar numbers exist in other bases too.

For this purpose, do the following:

Let's start with the solution:

USING: io kernel lists lists.lazy locals math math.functions
math.ranges prettyprint sequences ;

:: kaprekar? ( n -- ? )
    n sq :> sqr
    1 lfrom
    [ 10 swap ^ ] lmap-lazy
    [ n > ] lfilter
    [ sqr swap mod n < ] lwhile
    list>array
    [ 1 - sqr n - swap mod zero? ] any?
    n 1 = or ;

1,000,000 [1,b] [ kaprekar? ] filter dup . length
"Count of Kaprekar numbers <= 1,000,000: " write .