REVERSAL-ADDITION PALINDROME TEST ON 800067199

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 800067199:
800067199
+ 991760008
step 1: 1791827207
+ 7027281971
step 2: 8819109178
+ 8719019188
step 3: 17538128366
+ 66382183571
step 4: 83920311937
+ 73911302938
step 5: 157831614875
+ 578416138751
step 6: 736247753626
+ 626357742637
step 7: 1362605496263
+ 3626945062631
step 8: 4989550558894
+ 4988550559894
step 9: 9978101118788
+ 8878111018799
step 10: 18856212137587
+ 78573121265881
step 11: 97429333403468
+ 86430433392479
step 12: 183859766795947
+ 749597667958381
step 13: 933457434754328
+ 823457434754339
step 14: 1756914869508667
+ 7668059684196571
step 15: 9424974553705238
+ 8325073554794249
step 16: 17750048108499487
+ 78499480184005771
step 17: 96249528292505258
+ 85250529282594269
step 18: 181500057575099527
+ 725990575750005181
step 19: 907490633325104708
+ 807401523336094709
step 20: 1714892156661199417
+ 7149911666512984171
step 21: 8864803823174183588
+ 8853814713283084688
step 22: 17718618536457268276
+ 67286275463581681771
step 23: 85004894000038950047
+ 74005983000049840058
step 24: 159010877000088790105
+ 501097880000778010951
step 25: 660108757000866801056
+ 650108668000757801066
step 26: 1310217425001624602122
+ 2212064261005247120131
step 27: 3522281686006871722253
+ 3522271786006861822253
step 28: 7044553472013733544506
+ 6054453373102743554407
step 29: 13099006845116477098913
+ 31989077461154860099031
step 30: 45088084306271337197944
+ 44979173317260348088054
step 31: 90067257623531685285998
+ 89958258613532675276009
step 32: 180025516237064360562007
+ 700265063460732615520081
step 33: 880290579697796976082088
+ 880280679697796975092088
step 34: 1760571259395593951174176
+ 6714711593955939521750671
step 35: 8475282853351533472924847
+ 7484292743351533582825748
step 36: 15959575596703067055750595
+ 59505755076030769557595951
step 37: 75465330672733836613346546
+ 64564331663833727603356457
step 38: 140029662336567564216703003
+ 300307612465765633266920041
step 39: 440337274802333197483623044
+ 440326384791333208472733044
step 40: 880663659593666405956356088
+ 880653659504666395956366088
step 41: 1761317319098332801912722176
+ 6712272191082338909137131671
step 42: 8473589510180671711049853847
+ 7483589401171760810159853748
step 43: 15957178911352432521209707595
+ 59570790212523425311987175951
step 44: 75527969123875857833196883546
+ 64538869133875857832196972557
step 45: 140066838257751715665393856103
+ 301658393566517157752838660041
step 46: 441725231824268873418232516144
+ 441615232814378862428132527144
step 47: 883340464638647735846365043288
+ 882340563648537746836464043388
step 48: 1765681028287185482682829086676
+ 6766809282862845817828201865671
step 49: 8532490311150031300511030952347
+ 7432590301150031300511130942358
step 50: 15965080612300062601022161894705
+ 50749816122010626000321608056951
step 51: 66714896734310688601343769951656
+ 65615996734310688601343769841766
step 52: 132330893468621377202687539793422
+ 224397935786202773126864398033231
step 53: 356728829254824150329551937826653
+ 356628739155923051428452928827653
step 54: 713357568410747201758004866654306
+ 603456668400857102747014865753317
step 55: 1316814236811604304505019732407623
+ 3267042379105054034061186324186131
step 56: 4583856615916658338566206056593754
+ 4573956506026658338566195166583854
step 57: 9157813121943316677132401223177608
+ 8067713221042317766133491213187519
step 58: 17225526342985634443265892436365127
+ 72156363429856234443658924362552271
step 59: 89381889772841868886924816798917398
+ 89371989761842968886814827798818398
step 60: 178753879534684837773739644597735796
+ 697537795446937377738486435978357871
step 61: 876291674981622215512226080576093667
+ 766390675080622215512226189476192678
step 62: 1642682350062244431024452270052286345
+ 5436822500722544201344422600532862461
step 63: 7079504850784788632368874870585148806
+ 6088415850784788632368874870584059707
step 64: 13167920701569577264737749741169208513
+ 31580296114794773746277596510702976131
step 65: 44748216816364351011015346251872184644
+ 44648127815264351011015346361861284744
step 66: 89396344631628702022030692613733469388
+ 88396433731629603022020782613644369398
step 67: 177792778363258305044051475227377838786
+ 687838773722574150440503852363877297771
step 68: 865631552085832455484555327591255136557
+ 755631552195723555484554238580255136568
step 69: 1621263104281556010969109566171510273125
+ 5213720151716659019690106551824013621261
step 70: 6834983255998215030659216117995523894386
+ 6834983255997116129560305128995523894386
step 71: 13669966511995331160219521246991047788772
+ 27788774019964212591206113359911566996631
step 72: 41458740531959543751425634606902614785403
+ 30458741620960643652415734595913504785414
step 73: 71917482152920187403841369202816119570817
+ 71807591161820296314830478102925128471917
step 74: 143725073314740483718671847305741248042734
+ 437240842147503748176817384047413370527341
step 75: 580965915462244231895489231353154618570075
+ 570075816451353132984598132442264519569085
step 76: 1151041731913597364880087363795419138139160
+ 0619318319145973637800884637953191371401511
step 77: 1770360051059571002680972001748610509540671
+ 1760459050168471002790862001759501500630771
step 78: 3530819101228042005471834003508112010171442
+ 2441710102118053004381745002408221019180353
step 79: 5972529203346095009853579005916333029351795
+ 5971539203336195009753589005906433029252795
step 80: 11944068406682290019607168011822766058604590
+ 09540685066722811086170691009228660486044911
step 81: 21484753473405101105777859021051426544649501
+ 10594644562415012095877750110150437435748412
step 82: 32079398035820113201655609131201863980397913
+ 31979308936810213190655610231102853089397023
step 83: 64058706972630326392311219362304717069794936
+ 63949796071740326391211329362303627960785046
step 84: 128008503044370652783522548724608345030579982
+ 289975030543806427845225387256073440305800821
step 85: 417983533588177080628747935980681785336380803
+ 308083633587186089539747826080771885335389714
step 86: 726067167175363170168495762061453670671770517
+ 715077176076354160267594861071363571761760627
step 87: 1441144343251717330436090623132817242433531144
+ 4411353342427182313260906340337171523434411441
step 88: 5852497685678899643696996963469988765867942585
800067199 takes 88 iterations / steps to resolve into a 46 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 1,734,385 times since Saturday, March 9th, 2002.)