REVERSAL-ADDITION PALINDROME TEST ON 20889

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 20889:
20889
+ 98802
step 1: 119691
+ 196911
step 2: 316602
+ 206613
step 3: 523215
+ 512325
step 4: 1035540
+ 0455301
step 5: 1490841
+ 1480941
step 6: 2971782
+ 2871792
step 7: 5843574
+ 4753485
step 8: 10597059
+ 95079501
step 9: 105676560
+ 065676501
step 10: 171353061
+ 160353171
step 11: 331706232
+ 232607133
step 12: 564313365
+ 563313465
step 13: 1127626830
+ 0386267211
step 14: 1513894041
+ 1404983151
step 15: 2918877192
+ 2917788192
step 16: 5836665384
+ 4835666385
step 17: 10672331769
+ 96713327601
step 18: 107385659370
+ 073956583701
step 19: 181342243071
+ 170342243181
step 20: 351684486252
+ 252684486153
step 21: 604368972405
+ 504279863406
step 22: 1108648835811
+ 1185388468011
step 23: 2294037303822
+ 2283037304922
step 24: 4577074608744
+ 4478064707754
step 25: 9055139316498
+ 8946139315509
step 26: 18001278632007
+ 70023687210081
step 27: 88024965842088
+ 88024856942088
step 28: 176049822784176
+ 671487228940671
step 29: 847537051724847
+ 748427150735748
step 30: 1595964202460595
+ 5950642024695951
step 31: 7546606227156546
+ 6456517226066457
step 32: 14003123453223003
+ 30032235432130041
step 33: 44035358885353044
20889 takes 33 iterations / steps to resolve into a 17 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 1,734,372 times since Saturday, March 9th, 2002.)