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 there 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.

Example: 10000 (100²) splitting from left to right: The first split is [ ,10000], which is OK because "a conceptual single split...before the first digit that produces one empty string does have the empty string counted" (that is how 1 is a Kaprekar number). The second split is [1, 0000], which is not OK because "a split of all zeroes is not counted - as zero is not considered positive". Slight optimization opportunity: When splitting from left to right, once the right part becomes all zeroes, you don't need to test this number anymore because its splits will always be invalid.

J

Solution: <lang j>kapbase=: 0,.10 ^ 1 + [: i. 1 + 10 <.@^. >.&1 isKap=: 1 e. (((0 < {:"1@]) *. [ = +/"1@]) (kapbase #: ])@*:)</lang>

Example use:

<lang j> I. isKap"0 i.1e6 1 9 45 55 99 297 703 999 2223 2728 4879 4950 5050 5292 7272 7777 9999 17344 22222 38962 77778 82656 95121 99999 142857 148149 181819 187110 208495 318682 329967 351352 356643 390313 461539 466830 499500 500500 533170 538461 609687 627615 643357 648648 670033 681318 791505 812890 818181 851851 857143 961038 994708 999999</lang>

Alternative solution: The following is a more naive, mechanical solution <lang j>splitNum=: {. ,&(_&".) }. allSplits=: (i.&.<:@# splitNum"0 1 ])@": sumValidSplits=: [: +/"1 ] #~ 0 -.@e."1 ] filterKaprekar=: #~ ] e."0 1 [: sumValidSplits@allSplits"0 *:</lang>

Example use: <lang j> filterKaprekar i. 10000 0 9 45 55 99 297 703 999 2223 2728 4879 4950 5050 5292 7272 7777 9999

  #filterKaprekar i. 1e6

54</lang>

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){
       int count = 0;
       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);
                   count++;
                   break;
               }
           }
       }
       System.out.println(count + " Kaprekar numbers < 1000000");
   }

}</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
54 Kaprekar numbers < 1000000

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