REVERSAL-ADDITION PALINDROME TEST ON 13697

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 13697:
13697
+ 79631
step 1: 93328
+ 82339
step 2: 175667
+ 766571
step 3: 942238
+ 832249
step 4: 1774487
+ 7844771
step 5: 9619258
+ 8529169
step 6: 18148427
+ 72484181
step 7: 90632608
+ 80623609
step 8: 171256217
+ 712652171
step 9: 883908388
+ 883809388
step 10: 1767717776
+ 6777177671
step 11: 8544895447
+ 7445984458
step 12: 15990879905
+ 50997809951
step 13: 66988689856
+ 65898688966
step 14: 132887378822
+ 228873788231
step 15: 361761167053
+ 350761167163
step 16: 712522334216
+ 612433225217
step 17: 1324955559433
+ 3349555594231
step 18: 4674511153664
+ 4663511154764
step 19: 9338022308428
+ 8248032208339
step 20: 17586054516767
+ 76761545068571
step 21: 94347599585338
+ 83358599574349
step 22: 177706199159687
+ 786951991607771
step 23: 964658190767458
+ 854767091856469
step 24: 1819425282623927
+ 7293262825249181
step 25: 9112688107873108
+ 8013787018862119
step 26: 17126475126735227
+ 72253762157462171
step 27: 89380237284197398
+ 89379148273208398
step 28: 178759385557405796
+ 697504755583957871
step 29: 876264141141363667
+ 766363141141462678
step 30: 1642627282282826345
+ 5436282822827262461
step 31: 7078910105110088806
+ 6088800115010198707
step 32: 13167710220120287513
+ 31578202102201776131
step 33: 44745912322322063644
+ 44636022322321954744
step 34: 89381934644644018388
+ 88381044644643918398
step 35: 177762979289287936786
+ 687639782982979267771
step 36: 865402762272267204557
+ 755402762272267204568
step 37: 1620805524544534409125
+ 5219044354454255080261
step 38: 6839849878998789489386
13697 takes 38 iterations / steps to resolve into a 22 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 1,767,545 times since Saturday, March 9th, 2002.)