REVERSALADDITION
PALINDROME
TEST ON
10971

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 10971: 
10971
+ 17901
step 1: 28872
+ 27882
step 2: 56754
+ 45765
step 3: 102519
+ 915201
step 4: 1017720
+ 0277101
step 5: 1294821
+ 1284921
step 6: 2579742
+ 2479752
step 7: 5059494
+ 4949505
step 8: 10008999
+ 99980001
step 9: 109989000
+ 000989901
step 10: 110978901
+ 109879011
step 11: 220857912
+ 219758022
step 12: 440615934
+ 439516044
step 13: 880131978
+ 879131088
step 14: 1759263066
+ 6603629571
step 15: 8362892637
+ 7362982638
step 16: 15725875275
+ 57257852751
step 17: 72983728026
+ 62082738927
step 18: 135066466953
+ 359664660531
step 19: 494731127484
+ 484721137494
step 20: 979452264978
+ 879462254979
step 21: 1858914519957
+ 7599154198581
step 22: 9458068718538
+ 8358178608549
step 23: 17816247327087
+ 78072374261871
step 24: 95888621588958
+ 85988512688859
step 25: 181877134277817
+ 718772431778181
step 26: 900649566055998
+ 899550665946009
step 27: 1800200232002007
+ 7002002320020081
step 28: 8802202552022088


10971 takes 28 iterations / steps to resolve into a 16 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 1,886,748 times since Saturday, March 9^{th}, 2002.)
