REVERSALADDITION
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.

REVERSALADDITION
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 18digit numbers that resolve in 232 iterations,
higher than the 228 iteration record shown for 18digit numbers, but they were not recorded,
as a smaller [17digit] number already holds the record for 232 iterations.)
Digits  Number  Result 
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 2,132,393 times since Saturday, March 9^{th}, 2002.)
