REVERSAL-ADDITION PALINDROME TEST ON 89

Reverse and Add Process:

1. Pick a number.
2. Reverse its digits and add this value to the original number.
3. If this is not a palindrome, go back to step 2 and repeat.
Let's view this Reverse and Add sequence starting with 89:
 89 + 98 step 1: 187 + 781 step 2: 968 + 869 step 3: 1837 + 7381 step 4: 9218 + 8129 step 5: 17347 + 74371 step 6: 91718 + 81719 step 7: 173437 + 734371 step 8: 907808 + 808709 step 9: 1716517 + 7156171 step 10: 8872688 + 8862788 step 11: 17735476 + 67453771 step 12: 85189247 + 74298158 step 13: 159487405 + 504784951 step 14: 664272356 + 653272466 step 15: 1317544822 + 2284457131 step 16: 3602001953 + 3591002063 step 17: 7193004016 + 6104003917 step 18: 13297007933 + 33970079231 step 19: 47267087164 + 46178076274 step 20: 93445163438 + 83436154439 step 21: 176881317877 + 778713188671 step 22: 955594506548 + 845605495559 step 23: 1801200002107 + 7012000021081 step 24: 8813200023188
89 takes 24 iterations / steps to resolve into a 13 digit palindrome.

 REVERSAL-ADDITION PALINDROME RECORDS

Most Delayed Palindromic Number for each digit length
(Only iteration counts for which no smaller records exist are considered. My program records only the smallest number that resolves for each distinct iteration count. For example, there are 18-digit numbers that resolve in 232 iterations, higher than the 228 iteration record shown for 18-digit numbers, but they were not recorded, as a smaller [17-digit] number already holds the record for 232 iterations.)

DigitsNumberResult
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
89
187
1,297
10,911
150,296
9,008,299
10,309,988
140,669,390
1,005,499,526
10,087,799,570
100,001,987,765
1,600,005,969,190
14,104,229,999,995
100,120,849,299,260
1,030,020,097,997,900
10,442,000,392,399,960
170,500,000,303,619,996
1,186,060,307,891,929,990
solves in 24 iterations.
solves in 23 iterations.
solves in 21 iterations.
solves in 55 iterations.
solves in 64 iterations.
solves in 96 iterations.
solves in 95 iterations.
solves in 98 iterations.
solves in 109 iterations.
solves in 149 iterations.
solves in 143 iterations.
solves in 188 iterations.
solves in 182 iterations.
solves in 201 iterations.
solves in 197 iterations.
solves in 236 iterations.
solves in 228 iterations.
solves in 261 iterations - World Record!
[View all records]

This reverse and add program was created by Jason Doucette.
Please visit my Palindromes and World Records page.
You have permission to use the data from this webpage (with due credit).
A link to my website is much appreciated. Thank you.

(This program has been run 2,522,300 times since Saturday, March 9th, 2002.)