REVERSAL-ADDITION PALINDROME TEST ON 15891

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 15891:
15891
+ 19851
step 1: 35742
+ 24753
step 2: 60495
+ 59406
step 3: 119901
+ 109911
step 4: 229812
+ 218922
step 5: 448734
+ 437844
step 6: 886578
+ 875688
step 7: 1762266
+ 6622671
step 8: 8384937
+ 7394838
step 9: 15779775
+ 57797751
step 10: 73577526
+ 62577537
step 11: 136155063
+ 360551631
step 12: 496706694
+ 496607694
step 13: 993314388
+ 883413399
step 14: 1876727787
+ 7877276781
step 15: 9754004568
+ 8654004579
step 16: 18408009147
+ 74190080481
step 17: 92598089628
+ 82698089529
step 18: 175296179157
+ 751971692571
step 19: 927267871728
+ 827178762729
step 20: 1754446634457
+ 7544366444571
step 21: 9298813079028
+ 8209703188929
step 22: 17508516267957
+ 75976261580571
step 23: 93484777848528
+ 82584877748439
step 24: 176069655596967
+ 769695556960671
step 25: 945765212557638
+ 836755212567549
step 26: 1782520425125187
+ 7815215240252871
step 27: 9597735665378058
+ 8508735665377959
step 28: 18106471330756017
+ 71065703317460181
step 29: 89172174648216198
+ 89161284647127198
step 30: 178333459295343396
+ 693343592954333871
step 31: 871677052249677267
+ 762776942250776178
step 32: 1634453994500453445
+ 5443540054993544361
step 33: 7077994049493997806
+ 6087993949404997707
step 34: 13165987998898995513
+ 31559989889978956131
step 35: 44725977888877951644
+ 44615977888877952744
step 36: 89341955777755904388
+ 88340955777755914398
step 37: 177682911555511818786
+ 687818115555119286771
step 38: 865501027110631105557
+ 755501136011720105568
step 39: 1621002163122351211125
+ 5211121532213612001261
step 40: 6832123695335963212386
15891 takes 40 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 1,768,549 times since Saturday, March 9th, 2002.)