REVERSAL-ADDITION PALINDROME TEST ON 100055896

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 100055896:
100055896
+ 698550001
step 1: 798605897
+ 798506897
step 2: 1597112794
+ 4972117951
step 3: 6569230745
+ 5470329656
step 4: 12039560401
+ 10406593021
step 5: 22446153422
+ 22435164422
step 6: 44881317844
+ 44871318844
step 7: 89752636688
+ 88663625798
step 8: 178416262486
+ 684262614871
step 9: 862678877357
+ 753778876268
step 10: 1616457753625
+ 5263577546161
step 11: 6880035299786
+ 6879925300886
step 12: 13759960600672
+ 27600606995731
step 13: 41360567596403
+ 30469576506314
step 14: 71830144102717
+ 71720144103817
step 15: 143550288206534
+ 435602882055341
step 16: 579153170261875
+ 578162071351975
step 17: 1157315241613850
+ 0583161425137511
step 18: 1740476666751361
+ 1631576666740471
step 19: 3372053333491832
+ 2381943333502733
step 20: 5753996666994565
+ 5654996666993575
step 21: 11408993333988140
+ 04188933339980411
step 22: 15597926673968551
+ 15586937662979551
step 23: 31184864336948102
+ 20184963346848113
step 24: 51369827683796215
+ 51269738672896315
step 25: 102639566356692530
+ 035296653665936201
step 26: 137936220022628731
+ 137826220022639731
step 27: 275762440045268462
+ 264862540044267572
step 28: 540624980089536034
+ 430635980089426045
step 29: 971260960178962079
+ 970269871069062179
step 30: 1941530831248024258
+ 8524208421380351491
step 31: 10465739252628375749
+ 94757382625293756401
step 32: 105223121877922132150
+ 051231229778121322501
step 33: 156454351656043454651
+ 156454340656153454651
step 34: 312908692312196909302
+ 203909691213296809213
step 35: 516818383525493718515
+ 515817394525383818615
step 36: 1032635778050877537130
+ 0317357780508775362301
step 37: 1349993558559652899431
+ 1349982569558553999431
step 38: 2699976128118206898862
+ 2688986028118216799962
step 39: 5388962156236423698824
+ 4288963246326512698835
step 40: 9677925402562936397659
+ 9567936392652045297769
step 41: 19245861795214981695428
+ 82459618941259716854291
step 42: 101705480736474698549719
+ 917945896474637084507101
step 43: 1019651377211111783056820
+ 0286503871111127731569101
step 44: 1306155248322239514625921
+ 1295264159322238425516031
step 45: 2601419407644477940141952
+ 2591410497744467049141062
step 46: 5192829905388944989283014
+ 4103829894498835099282915
step 47: 9296659799887780088565929
+ 9295658800877889979566929
step 48: 18592318600765670068132858
+ 85823186007656700681329581
step 49: 104415504608422370749462439
+ 934264947073224806405514401
step 50: 1038680451681647177154976840
+ 0486794517717461861540868301
step 51: 1525474969399109038695845141
+ 1415485968309019939694745251
step 52: 2940960937708128978390590392
+ 2930950938798218077390690492
step 53: 5871911876506347055781280884
+ 4880821875507436056781191785
step 54: 10752733752013783112562472669
+ 96627426521138731025733725701
step 55: 107380160273152514138296198370
+ 073891692831415251372061083701
step 56: 181271853104567765510357282071
+ 170282753015567765401358172181
step 57: 351554606120135530911715454252
+ 252454517119035531021606455153
step 58: 604009123239171061933321909405
+ 504909123339160171932321900406
step 59: 1108918246578331233865643809811
+ 1189083465683321338756428198011
step 60: 2298001712261652572622072007822
+ 2287002702262752561622171008922
step 61: 4585004414524405134244243016744
+ 4476103424424315044254144005854
step 62: 9061107838948720178498387022598
+ 8952207838948710278498387011609
step 63: 18013315677897430456996774034207
+ 70243047769965403479877651331081
step 64: 88256363447862833936874425365288
+ 88256352447863933826874436365288
step 65: 176512715895726767763748861730576
+ 675037168847367767627598517215671
step 66: 851549884743094535391347378946247
+ 742649873743193535490347488945158
step 67: 1594199758486288070881694867891405
+ 5041987684961880708826848579914951
step 68: 6636187443448168779708543447806356
+ 6536087443458079778618443447816366
step 69: 13172274886906248558326986895622722
+ 22722659868962385584260968847227131
step 70: 35894934755868634142587955742849853
+ 35894824755978524143686855743949853
step 71: 71789759511847158286274811486799706
+ 60799768411847268285174811595798717
step 72: 132589527923694426571449623082598423
+ 324895280326944175624496329725985231
step 73: 457484808250638602195945952808583654
+ 456385808259549591206836052808484754
step 74: 913870616510188193402782005617068408
+ 804860716500287204391881015616078319
step 75: 1718731333010475397794663021233146727
+ 7276413321203664977935740103331378171
step 76: 8995144654214140375730403124564524898
+ 8984254654213040375730414124564415998
step 77: 17979399308427180751460817249128940896
+ 69804982194271806415708172480399397971
step 78: 87784381502698987167168989729528338867
+ 76883382592798986176178989620518348778
step 79: 164667764095497973343347979350046687645
+ 546786640053979743343379794590467766461
step 80: 711454404149477716686727773940514454106
+ 601454415049377727686617774941404454117
step 81: 1312908819198855444373345548881918908223
+ 3228098191888455433734445588919188092131
step 82: 4541007011087310878107791137801107000354
+ 4530007011087311977018780137801107001454
step 83: 9071014022174622855126571275602214001808
+ 8081004122065721756215582264712204101709
step 84: 17152018144240344611342153540314418103517
+ 71530181441304535124311644304244181025171
step 85: 88682199585544879735653797844558599128688
100055896 takes 85 iterations / steps to resolve into a 41 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 1,717,148 times since Saturday, March 9th, 2002.)