REVERSAL-ADDITION PALINDROME TEST ON 10029826

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 10029826:
10029826
+ 62892001
step 1: 72921827
+ 72812927
step 2: 145734754
+ 457437541
step 3: 603172295
+ 592271306
step 4: 1195443601
+ 1063445911
step 5: 2258889512
+ 2159888522
step 6: 4418778034
+ 4308778144
step 7: 8727556178
+ 8716557278
step 8: 17444113456
+ 65431144471
step 9: 82875257927
+ 72975257828
step 10: 155850515755
+ 557515058551
step 11: 713365574306
+ 603475563317
step 12: 1316841137623
+ 3267311486131
step 13: 4584152623754
+ 4573262514854
step 14: 9157415138608
+ 8068315147519
step 15: 17225730286127
+ 72168203752271
step 16: 89393934038398
+ 89383043939398
step 17: 178776977977796
+ 697779779677871
step 18: 876556757655667
+ 766556757655678
step 19: 1643113515311345
+ 5431135153113461
step 20: 7074248668424806
+ 6084248668424707
step 21: 13158497336849513
+ 31594863379485131
step 22: 44753360716334644
+ 44643361706335744
step 23: 89396722422670388
+ 88307622422769398
step 24: 177704344845439786
+ 687934548443407771
step 25: 865638893288847557
+ 755748882398836568
step 26: 1621387775687684125
+ 5214867865777831261
step 27: 6836255641465515386
+ 6835155641465526386
step 28: 13671411282931041772
+ 27714013928211417631
step 29: 41385425211142459403
+ 30495424111252458314
step 30: 71880849322394917717
+ 71771949322394808817
step 31: 143652798644789726534
+ 435627987446897256341
step 32: 579280786091686982875
+ 578289686190687082975
step 33: 1157570472282374065850
+ 0585604732822740757511
step 34: 1743175205105114823361
+ 1633284115015025713471
step 35: 3376459320120140536832
+ 2386350410210239546733
step 36: 5762809730330380083565
+ 5653800830330379082675
step 37: 11416610560660759166240
+ 04266195706606501661411
step 38: 15682806267267260827651
+ 15672806276276260828651
step 39: 31355612543543521656302
+ 20365612534534521655313
step 40: 51721225078078043311615
+ 51611334087087052212715
step 41: 103332559165165095524330
+ 033425590561561955233301
step 42: 136758149726727050757631
+ 136757050727627941857631
step 43: 273515200454354992615262
+ 262516299453454002515372
step 44: 536031499907808995130634
+ 436031599808709994130635
step 45: 972063099716518989261269
+ 962162989815617990360279
step 46: 1934226089532136979621548
+ 8451269796312359806224391
step 47: 10385495885844496785845939
+ 93954858769444858859458301
step 48: 104340354655289355645304240
+ 042403546553982556453043401
step 49: 146743901209271912098347641
+ 146743890219172902109347641
step 50: 293487791428444814207695282
+ 282596702418444824197784392
step 51: 576084493846889638405479674
+ 476974504836988648394480675
step 52: 1053058998683878286799960349
+ 9430699976828783868998503501
step 53: 10483758975512662155798463850
+ 05836489755126621557985738401
step 54: 16320248730639283713784202251
+ 15220248731738293603784202361
step 55: 31540497462377577317568404612
+ 21640486571377577326479404513
step 56: 53180984033755154644047809125
+ 52190874044645155733048908135
step 57: 105371858078400310377096717260
+ 062717690773013004870858173501
step 58: 168089548851413315247954890761
+ 167098459742513314158845980861
step 59: 335188008593926629406800871622
+ 226178008604926629395800881533
step 60: 561366017198853258802601753155
+ 551357106208852358891710663165
step 61: 1112723123407705617694312416320
+ 0236142134967165077043213272111
step 62: 1348865258374870694737525688431
+ 1348865257374960784738525688431
step 63: 2697730515749831479476051376862
+ 2686731506749741389475150377962
step 64: 5384462022499572868951201754824
+ 4284571021598682759942202644835
step 65: 9669033044098255628893404399659
+ 9569934043988265528904403309669
step 66: 19238967088086521157797807709328
+ 82390770879775112568088076983291
step 67: 101629737967861633725885884692619
+ 916296488588527336168769737926101
step 68: 1017926226556388969894655622618720
+ 0278162265564989698836556226297101
step 69: 1296088492121378668731211848915821
+ 1285198481121378668731212948806921
step 70: 2581286973242757337462424797722742
+ 2472277974242647337572423796821852
step 71: 5053564947485404675034848594544594
+ 4954454958484305764045847494653505
step 72: 10008019905969710439080696089198099
+ 99089198069608093401796950991080001
step 73: 109097217975577803840877647080278100
+ 001872080746778048308775579712790901
step 74: 110969298722355852149653226793069001
+ 100960397622356941258553227892969011
step 75: 211929696344712793408206454686038012
+ 210830686454602804397217443696929112
step 76: 422760382799315597805423898382967124
+ 421769283898324508795513997283067224
step 77: 844529666697640106600937895666034348
+ 843430666598739006601046796666925448
step 78: 1687960333296379113201984692332959796
+ 6979592332964891023119736923330697861
step 79: 8667552666261270136321721615663657657
+ 7567563665161271236310721626662557668
step 80: 16235116331422541372632443242326215325
+ 52351262324234423627314522413361153261
step 81: 68586378655656964999946965655687368586
10029826 takes 81 iterations / steps to resolve into a 38 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 1,749,545 times since Saturday, March 9th, 2002.)