# Program: Number Palindromes

My wife, Betty, recently reminded me of a theorem that I must have studied in high school but whose name I have long since forgotten: that any positive integer number can be used to generate a palindrome by adding to it the number comprised of its digits in reverse order. Palindromes are sequences that read the same in either direction, such as the name “Anna” or the phrase “Madam, I’m Adam” (being non-strict and ignoring spaces and punctuation). We normally think of palindromes as composed of text, but the concept can be applied to numbers: 13531 is a palindrome. Start with the number 72, for example, and add to it the number 27. The results of this addition is 99, which is a (short) palindrome. Starting with 142, add 241, and you get 383. Some numbers take more than one try to generate a palindrome. 1951 + 1591 yields 3542, which is not palindromic. The second round, however, 3542 + 2453, yields 5995, which is. The number 17,892, which my son Benjamin picked out of the air, requires 12 rounds to generate a palindrome, but it does terminate:

```C:\javasrc\numbers>java  Palindrome 72 142 1951 17892
Trying 72
72->99
Trying 142
142->383
Trying 1951
Trying 3542
1951->5995
Trying 17892
Trying 47763
Trying 84537
Trying 158085
Trying 738936
Trying 1378773
Trying 5157504
Trying 9215019
Trying 18320148
Trying 102422529
Trying 1027646730
Trying 1404113931
17892->2797227972

C:\javasrc\numbers>```

If this sounds to you like a natural candidate for recursion, you are ...

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