Kaprekar numbers

Kaprekar numbers is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

A positive integer is a Kaprekar number if the string representation of its square can be split once into parts that when summed add up to the original number.

For example 2223 is a Kaprekar number as 2223*2223 == 4941729 and 494 + 1729 == 2223

The series of kaprekar numbers begins: 1, 9, 45, 55, ....

The task is to generate and show all the Kaprekar numbers less than 10,000

As a stretch goal count and show how many Kaprekar numbers their are that are less than one million.

Note: In comparing splits of the square, a split of all zeroes is not counted - as zero is not considered positive. However a conceptual single split at the very end or before the first digit that produces one empty string does have the empty string counted.

Java

<lang java>public class Kaprekar { private static String[] splitAt(String str, int idx){ String[] ans = new String[2]; ans[0] = str.substring(0, idx); if(ans[0].equals("")) ans[0] = "0"; //parsing "" throws an exception ans[1] = str.substring(idx); return ans; }

public static void main(String[] args){ for(long i = 1; i <= 1000000; i++){ String sqrStr = Long.toString(i * i); for(int j = 0; j < sqrStr.length(); j++){ String[] parts = splitAt(sqrStr, j); long firstNum = Long.parseLong(parts[0]); long secNum = Long.parseLong(parts[1]); //if the right part is all zeroes, then it will be forever, so break if(secNum == 0) break; if(firstNum + secNum == i){ System.out.println(i); break; } } } } }</lang> Output (shortened):

1
9
45
55
99
297
703
999
2223
2728
4879
4950
5050
5292
7272
7777
9999
...
818181
851851
857143
961038
994708
999999

Python

(Swap the commented return statement to return the split information). <lang python>>>> >>> def k(n): n2 = str(n**2) for i in range(len(n2)): a, b = int(n2[:i] or 0), int(n2[i:]) if b and a + b == n: return n #return (n, (n2[:i], n2[i:]))

>>> [x for x in range(1,10000) if k(x)] [1, 9, 45, 55, 99, 297, 703, 999, 2223, 2728, 4879, 4950, 5050, 5292, 7272, 7777, 9999] >>> len([x for x in range(1,1000000) if k(x)]) 54 >>> </lang>

Tcl

<lang tcl>package require Tcl 8.5; # Arbitrary precision arithmetic, for stretch goal only proc kaprekar n {

   if {$n == 1} {return 1}
   set s [expr {$n * $n}]
   for {set i 1} {$i < [string length $s]} {incr i} {

scan $s "%${i}d%d" a b if {$b && $n == $a + $b} { return 1 #return [list 1 $a $b] }

   }
   return 0

}

1. Base goal

for {set i 1} {$i < 10000} {incr i} {

   if {[kaprekar $i]} {lappend klist $i}

} puts [join $klist ", "]

1. Stretch goal

for {set i 1} {$i < 1000000} {incr i} {

   incr kcount [kaprekar $i]

} puts "$kcount Kaprekar numbers less than 1000000"</lang> Output:

1, 9, 45, 55, 99, 297, 703, 999, 2223, 2728, 4879, 4950, 5050, 5292, 7272, 7777, 9999
54 Kaprekar numbers less than 1000000