REVERSAL-ADDITION PALINDROME TEST ON 999

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 999:
999
+ 999
step 1: 1998
+ 8991
step 2: 10989
+ 98901
step 3: 109890
+ 098901
step 4: 208791
+ 197802
step 5: 406593
+ 395604
step 6: 802197
+ 791208
step 7: 1593405
+ 5043951
step 8: 6637356
+ 6537366
step 9: 13174722
+ 22747131
step 10: 35921853
+ 35812953
step 11: 71734806
+ 60843717
step 12: 132578523
+ 325875231
step 13: 458453754
+ 457354854
step 14: 915808608
+ 806808519
step 15: 1722617127
+ 7217162271
step 16: 8939779398
999 takes 16 iterations / steps to resolve into a 10 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 1,733,901 times since Saturday, March 9th, 2002.)