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                    REVERSAL-ADDITION PALINDROME TEST ON 151033997

                    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 151033997:
                    151033997
                    + 799330151
                    step 1: 950364148
                    + 841463059
                    step 2: 1791827207
                    + 7027281971
                    step 3: 8819109178
                    + 8719019188
                    step 4: 17538128366
                    + 66382183571
                    step 5: 83920311937
                    + 73911302938
                    step 6: 157831614875
                    + 578416138751
                    step 7: 736247753626
                    + 626357742637
                    step 8: 1362605496263
                    + 3626945062631
                    step 9: 4989550558894
                    + 4988550559894
                    step 10: 9978101118788
                    + 8878111018799
                    step 11: 18856212137587
                    + 78573121265881
                    step 12: 97429333403468
                    + 86430433392479
                    step 13: 183859766795947
                    + 749597667958381
                    step 14: 933457434754328
                    + 823457434754339
                    step 15: 1756914869508667
                    + 7668059684196571
                    step 16: 9424974553705238
                    + 8325073554794249
                    step 17: 17750048108499487
                    + 78499480184005771
                    step 18: 96249528292505258
                    + 85250529282594269
                    step 19: 181500057575099527
                    + 725990575750005181
                    step 20: 907490633325104708
                    + 807401523336094709
                    step 21: 1714892156661199417
                    + 7149911666512984171
                    step 22: 8864803823174183588
                    + 8853814713283084688
                    step 23: 17718618536457268276
                    + 67286275463581681771
                    step 24: 85004894000038950047
                    + 74005983000049840058
                    step 25: 159010877000088790105
                    + 501097880000778010951
                    step 26: 660108757000866801056
                    + 650108668000757801066
                    step 27: 1310217425001624602122
                    + 2212064261005247120131
                    step 28: 3522281686006871722253
                    + 3522271786006861822253
                    step 29: 7044553472013733544506
                    + 6054453373102743554407
                    step 30: 13099006845116477098913
                    + 31989077461154860099031
                    step 31: 45088084306271337197944
                    + 44979173317260348088054
                    step 32: 90067257623531685285998
                    + 89958258613532675276009
                    step 33: 180025516237064360562007
                    + 700265063460732615520081
                    step 34: 880290579697796976082088
                    + 880280679697796975092088
                    step 35: 1760571259395593951174176
                    + 6714711593955939521750671
                    step 36: 8475282853351533472924847
                    + 7484292743351533582825748
                    step 37: 15959575596703067055750595
                    + 59505755076030769557595951
                    step 38: 75465330672733836613346546
                    + 64564331663833727603356457
                    step 39: 140029662336567564216703003
                    + 300307612465765633266920041
                    step 40: 440337274802333197483623044
                    + 440326384791333208472733044
                    step 41: 880663659593666405956356088
                    + 880653659504666395956366088
                    step 42: 1761317319098332801912722176
                    + 6712272191082338909137131671
                    step 43: 8473589510180671711049853847
                    + 7483589401171760810159853748
                    step 44: 15957178911352432521209707595
                    + 59570790212523425311987175951
                    step 45: 75527969123875857833196883546
                    + 64538869133875857832196972557
                    step 46: 140066838257751715665393856103
                    + 301658393566517157752838660041
                    step 47: 441725231824268873418232516144
                    + 441615232814378862428132527144
                    step 48: 883340464638647735846365043288
                    + 882340563648537746836464043388
                    step 49: 1765681028287185482682829086676
                    + 6766809282862845817828201865671
                    step 50: 8532490311150031300511030952347
                    + 7432590301150031300511130942358
                    step 51: 15965080612300062601022161894705
                    + 50749816122010626000321608056951
                    step 52: 66714896734310688601343769951656
                    + 65615996734310688601343769841766
                    step 53: 132330893468621377202687539793422
                    + 224397935786202773126864398033231
                    step 54: 356728829254824150329551937826653
                    + 356628739155923051428452928827653
                    step 55: 713357568410747201758004866654306
                    + 603456668400857102747014865753317
                    step 56: 1316814236811604304505019732407623
                    + 3267042379105054034061186324186131
                    step 57: 4583856615916658338566206056593754
                    + 4573956506026658338566195166583854
                    step 58: 9157813121943316677132401223177608
                    + 8067713221042317766133491213187519
                    step 59: 17225526342985634443265892436365127
                    + 72156363429856234443658924362552271
                    step 60: 89381889772841868886924816798917398
                    + 89371989761842968886814827798818398
                    step 61: 178753879534684837773739644597735796
                    + 697537795446937377738486435978357871
                    step 62: 876291674981622215512226080576093667
                    + 766390675080622215512226189476192678
                    step 63: 1642682350062244431024452270052286345
                    + 5436822500722544201344422600532862461
                    step 64: 7079504850784788632368874870585148806
                    + 6088415850784788632368874870584059707
                    step 65: 13167920701569577264737749741169208513
                    + 31580296114794773746277596510702976131
                    step 66: 44748216816364351011015346251872184644
                    + 44648127815264351011015346361861284744
                    step 67: 89396344631628702022030692613733469388
                    + 88396433731629603022020782613644369398
                    step 68: 177792778363258305044051475227377838786
                    + 687838773722574150440503852363877297771
                    step 69: 865631552085832455484555327591255136557
                    + 755631552195723555484554238580255136568
                    step 70: 1621263104281556010969109566171510273125
                    + 5213720151716659019690106551824013621261
                    step 71: 6834983255998215030659216117995523894386
                    + 6834983255997116129560305128995523894386
                    step 72: 13669966511995331160219521246991047788772
                    + 27788774019964212591206113359911566996631
                    step 73: 41458740531959543751425634606902614785403
                    + 30458741620960643652415734595913504785414
                    step 74: 71917482152920187403841369202816119570817
                    + 71807591161820296314830478102925128471917
                    step 75: 143725073314740483718671847305741248042734
                    + 437240842147503748176817384047413370527341
                    step 76: 580965915462244231895489231353154618570075
                    + 570075816451353132984598132442264519569085
                    step 77: 1151041731913597364880087363795419138139160
                    + 0619318319145973637800884637953191371401511
                    step 78: 1770360051059571002680972001748610509540671
                    + 1760459050168471002790862001759501500630771
                    step 79: 3530819101228042005471834003508112010171442
                    + 2441710102118053004381745002408221019180353
                    step 80: 5972529203346095009853579005916333029351795
                    + 5971539203336195009753589005906433029252795
                    step 81: 11944068406682290019607168011822766058604590
                    + 09540685066722811086170691009228660486044911
                    step 82: 21484753473405101105777859021051426544649501
                    + 10594644562415012095877750110150437435748412
                    step 83: 32079398035820113201655609131201863980397913
                    + 31979308936810213190655610231102853089397023
                    step 84: 64058706972630326392311219362304717069794936
                    + 63949796071740326391211329362303627960785046
                    step 85: 128008503044370652783522548724608345030579982
                    + 289975030543806427845225387256073440305800821
                    step 86: 417983533588177080628747935980681785336380803
                    + 308083633587186089539747826080771885335389714
                    step 87: 726067167175363170168495762061453670671770517
                    + 715077176076354160267594861071363571761760627
                    step 88: 1441144343251717330436090623132817242433531144
                    + 4411353342427182313260906340337171523434411441
                    step 89: 5852497685678899643696996963469988765867942585
                    151033997 takes 89 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 2,095,940 times since Saturday, March 9th, 2002.)

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