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                    REVERSAL-ADDITION PALINDROME TEST ON 1009049407

                    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 1009049407:
                    1009049407
                    + 7049409001
                    step 1: 8058458408
                    + 8048548508
                    step 2: 16107006916
                    + 61960070161
                    step 3: 78067077077
                    + 77077076087
                    step 4: 155144153164
                    + 461351441551
                    step 5: 616495594715
                    + 517495594616
                    step 6: 1133991189331
                    + 1339811993311
                    step 7: 2473803182642
                    + 2462813083742
                    step 8: 4936616266384
                    + 4836626166394
                    step 9: 9773242432778
                    + 8772342423779
                    step 10: 18545584856557
                    + 75565848554581
                    step 11: 94111433411138
                    + 83111433411149
                    step 12: 177222866822287
                    + 782228668222771
                    step 13: 959451535045058
                    + 850540535154959
                    step 14: 1809992070200017
                    + 7100020702999081
                    step 15: 8910012773199098
                    + 8909913772100198
                    step 16: 17819926545299296
                    + 69299254562991871
                    step 17: 87119181108291167
                    + 76119280118191178
                    step 18: 163238461226482345
                    + 543284622164832361
                    step 19: 706523083391314706
                    + 607413193380325607
                    step 20: 1313936276771640313
                    + 3130461776726393131
                    step 21: 4444398053498033444
                    + 4443308943508934444
                    step 22: 8887706997006967888
                    + 8887696007996077888
                    step 23: 17775403005003045776
                    + 67754030050030457771
                    step 24: 85529433055033503547
                    + 74530533055033492558
                    step 25: 160059966110066996105
                    + 501699660011669950061
                    step 26: 661759626121736946166
                    + 661649637121626957166
                    step 27: 1323409263243363903332
                    + 2333093633423629043231
                    step 28: 3656502896666992946563
                    + 3656492996666982056563
                    step 29: 7312995893333975003126
                    + 6213005793333985992137
                    step 30: 13526001686667960995263
                    + 36259906976668610062531
                    step 31: 49785908663336571057794
                    + 49775017563336680958794
                    step 32: 99560926226673252016588
                    + 88561025237662262906599
                    step 33: 188121951464335514923187
                    + 781329415533464159121881
                    step 34: 969451366997799674045068
                    + 860540476997799663154969
                    step 35: 1829991843995599337200037
                    + 7300027339955993481999281
                    step 36: 9130019183951592819199318
                    + 8139919182951593819100319
                    step 37: 17269938366903186638299637
                    + 73699283668130966383996271
                    step 38: 90969222035034153022295908
                    + 80959222035143053022296909
                    step 39: 171928444070177206044592817
                    + 718295440602771070444829171
                    step 40: 890223884672948276489421988
                    + 889124984672849276488322098
                    step 41: 1779348869345797552977744086
                    + 6804477792557975439688439771
                    step 42: 8583826661903772992666183857
                    + 7583816662992773091666283858
                    step 43: 16167643324896546084332467715
                    + 51776423348064569842334676161
                    step 44: 67944066672961115926667143876
                    + 67834176662951116927666044976
                    step 45: 135778243335912232854333188852
                    + 258881333458232219533342877531
                    step 46: 394659576794144452387676066383
                    + 383660676783254441497675956493
                    step 47: 778320253577398893885352022876
                    + 678220253588398893775352023877
                    step 48: 1456540507165797787660704046753
                    + 3576404070667877975617050456541
                    step 49: 5032944577833675763277754503294
                    + 4923054577723675763387754492305
                    step 50: 9955999155557351526665508995599
                    + 9955998055666251537555519995599
                    step 51: 19911997211223603064221028991198
                    + 89119982012246030632211279911991
                    step 52: 109031979223469633696432308903189
                    + 981309803234696336964322979130901
                    step 53: 1090341782458165970660755288034090
                    + 0904308825570660795618542871430901
                    step 54: 1994650608028826766279298159464991
                    + 1994649518929726676288208060564991
                    step 55: 3989300126958553442567506220029982
                    + 2899200226057652443558596210039893
                    step 56: 6888500353016205886126102430069875
                    + 5789600342016216885026103530058886
                    step 57: 12678100695032422771152205960128761
                    + 16782106950225117722423059600187621
                    step 58: 29460207645257540493575265560316382
                    + 28361306556257539404575254670206492
                    step 59: 57821514201515079898150520230522874
                    + 47822503202505189897051510241512875
                    step 60: 105644017404020269795202030472035749
                    + 947530274030202597962020404710446501
                    step 61: 1053174291434222867757222435182482250
                    + 0522842815342227577682224341924713501
                    step 62: 1576017106776450445439446777107195751
                    + 1575917017776449345440546776017106751
                    step 63: 3151934124552899790879993553124302502
                    + 2052034213553999780979982554214391513
                    step 64: 5203968338106899571859976107338694015
                    + 5104968337016799581759986018338693025
                    step 65: 10308936675123699153619962125677387040
                    + 04078377652126991635199632157663980301
                    step 66: 14387314327250690788819594283341367341
                    + 14376314338249591888709605272341378341
                    step 67: 28763628665500282677529199555682745682
                    + 28654728655599192577628200556682636782
                    step 68: 57418357321099475255157400112365382464
                    + 46428356321100475155257499012375381475
                    step 69: 103846713642199950410414899124740763939
                    + 939367047421998414014059991246317648301
                    step 70: 1043213761064198364424474890371058412240
                    + 0422148501730984744244638914601673123401
                    step 71: 1465362262795183108669113804972731535641
                    + 1465351372794083119668013815972622635641
                    step 72: 2930713635589266228337127620945354171282
                    + 2821714535490267217338226629855363170392
                    step 73: 5752428171079533445675354250800717341674
                    + 4761437170080524535765443359701718242575
                    step 74: 10513865341160057981440797610502435584249
                    + 94248553420501679704418975006114356831501
                    step 75: 104762418761661737685859772616616792415750
                    + 057514297616616277958586737166167814267401
                    step 76: 162276716378278015644446509782784606683151
                    + 151386606487287905644446510872873617672261
                    step 77: 313663322865565921288893020655658224355412
                    + 214553422856556020398882129565568223366313
                    step 78: 528216745722121941687775150221226447721725
                    + 527127744622122051577786149121227547612825
                    step 79: 1055344490344243993265561299342453995334550
                    + 0554335993542439921655623993424430944435501
                    step 80: 1609680483886683914921185292766884939770051
                    + 1500779394886672925811294193866883840869061
                    step 81: 3110459878773356840732479486633768780639112
                    + 2119360878673366849742370486533778789540113
                    step 82: 5229820757446723690474849973167547570179225
                    + 5229710757457613799484740963276447570289225
                    step 83: 10459531514904337489959590936443995140468450
                    + 05486404159934463909595998473340941513595401
                    step 84: 15945935674838801399555589409784936654063851
                    + 15836045663948790498555599310883847653954951
                    step 85: 31781981338787591898111188720668784308018802
                    + 20881080348786602788111189819578783318918713
                    step 86: 52663061687574194686222378540247567626937515
                    + 51573962676574204587322268649147578616036625
                    step 87: 104237024364148399273544647189395146242974140
                    + 041479242641593981746445372993841463420732401
                    step 88: 145716267005742381019990020183236609663706541
                    + 145607366906632381020099910183247500762617541
                    step 89: 291323633912374762040089930366484110426324082
                    + 280423624011484663039980040267473219336323192
                    step 90: 571747257923859425080069970633957329762647274
                    + 472746267923759336079960080524958329752747175
                    step 91: 1044493525847618761160030051158915659515394449
                    + 9444935159565198511500300611678167485253944401
                    step 92: 10489428685412817272660330662837083144769338850
                    + 05883396744138073826603306627271821458682498401
                    step 93: 16372825429550891099263637290108904603451837251
                    + 15273815430640980109273636299019805592452827361
                    step 94: 31646640860191871208537273589128710195904664612
                    + 21646640959101782198537273580217819106804664613
                    step 95: 53293281819293653407074547169346529302709329225
                    + 52292390720392564396174547070435639291818239235
                    step 96: 105585672539686217803249094239782168594527568460
                    + 064865725495861287932490942308712686935276585501
                    step 97: 170451398035547505735740036548494855529804153961
                    + 169351408925558494845630047537505745530893154071
                    step 98: 339802806961106000581370084086000601060697308032
                    + 230803796060106000680480073185000601169608208933
                    step 99: 570606603021212001261850157271001202230305516965
                    + 569615503032202100172751058162100212120306606075
                    step 100: 1140222106053414101434601215433101414350612123040
                    + 0403212160534141013345121064341014143506012220411
                    step 101: 1543434266587555114779722279774115557856624343451
                    1009049407 takes 101 iterations / steps to resolve into a 49 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 2,095,818 times since Saturday, March 9th, 2002.)

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