REVERSAL-ADDITION PALINDROME TEST ON 600259

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 600259:
600259
+ 952006
step 1: 1552265
+ 5622551
step 2: 7174816
+ 6184717
step 3: 13359533
+ 33595331
step 4: 46954864
+ 46845964
step 5: 93800828
+ 82800839
step 6: 176601667
+ 766106671
step 7: 942708338
+ 833807249
step 8: 1776515587
+ 7855156771
step 9: 9631672358
+ 8532761369
step 10: 18164433727
+ 72733446181
step 11: 90897879908
+ 80997879809
step 12: 171895759717
+ 717957598171
step 13: 889853357888
+ 888753358988
step 14: 1778606716876
+ 6786176068771
step 15: 8564782785647
+ 7465872874658
step 16: 16030655660305
+ 50306655603061
step 17: 66337311263366
+ 66336211373366
step 18: 132673522636732
+ 237636225376231
step 19: 370309748012963
+ 369210847903073
step 20: 739520595916036
+ 630619595025937
step 21: 1370140190941973
+ 3791490910410731
step 22: 5161631101352704
+ 4072531011361615
step 23: 9234162112714319
+ 9134172112614329
step 24: 18368334225328648
+ 84682352243386381
step 25: 103050686468715029
+ 920517864686050301
step 26: 1023568551154765330
+ 0335674511558653201
step 27: 1359243062713418531
+ 1358143172603429531
step 28: 2717386235316848062
+ 2608486135326837172
step 29: 5325872370643685234
+ 4325863460732785235
step 30: 9651735831376470469
+ 9640746731385371569
step 31: 19292482562761842038
+ 83024816726528429291
step 32: 102317299289290271329
+ 923172092982992713201
step 33: 1025489392272282984530
+ 0354892822722939845201
step 34: 1380382214995222829731
+ 1379282225994122830831
step 35: 2759664440989345660562
+ 2650665439890444669572
step 36: 5410329880879790330134
+ 4310330979780889230145
step 37: 9720660860660679560279
+ 9720659760660680660279
step 38: 19441320621321360220558
+ 85502206312312602314491
step 39: 104943526933633962535049
+ 940535269336339625349401
step 40: 1045478796269973587884450
+ 0544887853799626978745401
step 41: 1590366650069600566629851
+ 1589266650069600566630951
step 42: 3179633300139201133260802
+ 2080623311029310033369713
step 43: 5260256611168511166630515
+ 5150366611158611166520625
step 44: 10410623222327122333151140
+ 04115133322172322232601401
step 45: 14525756544499444565752541
600259 takes 45 iterations / steps to resolve into a 26 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 1,716,971 times since Saturday, March 9th, 2002.)