REVERSAL-ADDITION PALINDROME TEST ON 10853

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 10853:
10853
+ 35801
step 1: 46654
+ 45664
step 2: 92318
+ 81329
step 3: 173647
+ 746371
step 4: 920018
+ 810029
step 5: 1730047
+ 7400371
step 6: 9130418
+ 8140319
step 7: 17270737
+ 73707271
step 8: 90978008
+ 80087909
step 9: 171065917
+ 719560171
step 10: 890626088
+ 880626098
step 11: 1771252186
+ 6812521771
step 12: 8583773957
+ 7593773858
step 13: 16177547815
+ 51874577161
step 14: 68052124976
+ 67942125086
step 15: 135994250062
+ 260052499531
step 16: 396046749593
+ 395947640693
step 17: 791994390286
+ 682093499197
step 18: 1474087889483
+ 3849887804741
step 19: 5323975694224
+ 4224965793235
step 20: 9548941487459
+ 9547841498459
step 21: 19096782985918
+ 81958928769091
step 22: 101055711755009
+ 900557117550101
step 23: 1001612829305110
+ 0115039282161001
step 24: 1116652111466111
+ 1116641112566111
step 25: 2233293224032222
+ 2222304223923322
step 26: 4455597447955544
10853 takes 26 iterations / steps to resolve into a 16 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 1,704,644 times since Saturday, March 9th, 2002.)