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                    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 2,095,939 times since Saturday, March 9th, 2002.)

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