REVERSALADDITION
PALINDROME
TEST ON
13297

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 13297: 
13297
+ 79231
step 1: 92528
+ 82529
step 2: 175057
+ 750571
step 3: 925628
+ 826529
step 4: 1752157
+ 7512571
step 5: 9264728
+ 8274629
step 6: 17539357
+ 75393571
step 7: 92932928
+ 82923929
step 8: 175856857
+ 758658571
step 9: 934515428
+ 824515439
step 10: 1759030867
+ 7680309571
step 11: 9439340438
+ 8340439349
step 12: 17779779787
+ 78797797771
step 13: 96577577558
+ 85577577569
step 14: 182155155127
+ 721551551281
step 15: 903706706408
+ 804607607309
step 16: 1708314313717
+ 7173134138071
step 17: 8881448451788
+ 8871548441888
step 18: 17752996893676
+ 67639869925771
step 19: 85392866819447
+ 74491866829358
step 20: 159884733648805
+ 508846337488951
step 21: 668731071137756
+ 657731170137866
step 22: 1326462241275622
+ 2265721422646231
step 23: 3592183663921853
+ 3581293663812953
step 24: 7173477327734806
+ 6084377237743717
step 25: 13257854565478523
+ 32587456545875231
step 26: 45845311111353754
+ 45735311111354854
step 27: 91580622222708608
+ 80680722222608519
step 28: 172261344445317127
+ 721713544443162271
step 29: 893974888888479398


13297 takes 29 iterations / steps to resolve into a 18 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 2,439,484 times since Saturday, March 9^{th}, 2002.)
