REVERSAL-ADDITION PALINDROME TEST ON 1058921

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 1058921:
1058921
+ 1298501
step 1: 2357422
+ 2247532
step 2: 4604954
+ 4594064
step 3: 9199018
+ 8109919
step 4: 17308937
+ 73980371
step 5: 91289308
+ 80398219
step 6: 171687527
+ 725786171
step 7: 897473698
+ 896374798
step 8: 1793848496
+ 6948483971
step 9: 8742332467
+ 7642332478
step 10: 16384664945
+ 54946648361
step 11: 71331313306
+ 60331313317
step 12: 131662626623
+ 326626266131
step 13: 458288892754
+ 457298882854
step 14: 915587775608
+ 806577785519
step 15: 1722165561127
+ 7211655612271
step 16: 8933821173398
+ 8933711283398
step 17: 17867532456796
+ 69765423576871
step 18: 87632956033667
+ 76633065923678
step 19: 164266021957345
+ 543759120662461
step 20: 708025142619806
+ 608916241520807
step 21: 1316941384140613
+ 3160414831496131
step 22: 4477356215636744
+ 4476365126537744
step 23: 8953721342174488
+ 8844712431273598
step 24: 17798433773448086
+ 68084437733489771
step 25: 85882871506937857
+ 75873960517828858
step 26: 161756832024766715
+ 517667420238657161
step 27: 679424252263423876
+ 678324362252424976
step 28: 1357748614515848852
+ 2588485154168477531
step 29: 3946233768684326383
+ 3836234868673326493
step 30: 7782468637357652876
+ 6782567537368642877
step 31: 14565036174726295753
+ 35759262747163056541
step 32: 50324298921889352294
+ 49225398812989242305
step 33: 99549697734878594599
+ 99549587843779694599
step 34: 199099285578658289198
+ 891982856875582990991
step 35: 1091082142454241280189
+ 9810821424542412801901
step 36: 10901903566996654082090
+ 09028045669966530910901
step 37: 19929949236963184992991
+ 19929948136963294992991
step 38: 39859897373926479985982
+ 28958997462937379895893
step 39: 68818894836863859881875
+ 57818895836863849881886
step 40: 126637790673727709763761
+ 167367907727376097736621
step 41: 294005698401103807500382
+ 283005708301104896500492
step 42: 577011406702208704000874
+ 478000407802207604110775
step 43: 1055011814504416308111649
+ 9461118036144054181105501
step 44: 10516129850648470489217150
+ 05171298407484605892161501
step 45: 15687428258133076381378651
+ 15687318367033185282478651
step 46: 31374746625166261663857302
+ 20375836616266152664747313
step 47: 51750583241432414328604615
+ 51640682341423414238505715
step 48: 103391265582855828567110330
+ 033011765828558285562193301
step 49: 136403031411414114129303631
+ 136303921411414114130304631
step 50: 272706952822828228259608262
+ 262806952822828228259607272
step 51: 535513905645656456519215534
+ 435512915654656546509315535
step 52: 971026821300313003028531069
+ 960135820300313003128620179
step 53: 1931162641600626006157151248
+ 8421517516006260061462611391
step 54: 10352680157606886067619762639
+ 93626791676068860675108625301
step 55: 103979471833675746742728387940
+ 049783827247647576338174979301
step 56: 153763299081323323080903367241
+ 142763309080323323180992367351
step 57: 296526608161646646261895734592
+ 295437598162646646161806625692
step 58: 591964206324293292423702360284
+ 482063207324292392423602469195
step 59: 1074027413648585684847304829479
+ 9749284037484865858463147204701
step 60: 10823311451133451543310452034180
+ 08143025401334515433115411332801
step 61: 18966336852467966976425863366981
1058921 takes 61 iterations / steps to resolve into a 32 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 1,750,281 times since Saturday, March 9th, 2002.)