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                    REVERSAL-ADDITION PALINDROME TEST ON 5020089949

                    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 5020089949:
                    5020089949
                    + 9499800205
                    step 1: 14519890154
                    + 45109891541
                    step 2: 59629781695
                    + 59618792695
                    step 3: 119248574390
                    + 093475842911
                    step 4: 212724417301
                    + 103714427212
                    step 5: 316438844513
                    + 315448834613
                    step 6: 631887679126
                    + 621976788136
                    step 7: 1253864467262
                    + 2627644683521
                    step 8: 3881509150783
                    + 3870519051883
                    step 9: 7752028202666
                    + 6662028202577
                    step 10: 14414056405243
                    + 34250465041441
                    step 11: 48664521446684
                    + 48664412546684
                    step 12: 97328933993368
                    + 86339933982379
                    step 13: 183668867975747
                    + 747579768866381
                    step 14: 931248636842128
                    + 821248636842139
                    step 15: 1752497273684267
                    + 7624863727942571
                    step 16: 9377361001626838
                    + 8386261001637739
                    step 17: 17763622003264577
                    + 77546230022636771
                    step 18: 95309852025901348
                    + 84310952025890359
                    step 19: 179620804051791707
                    + 707197150408026971
                    step 20: 886817954459818678
                    + 876818954459718688
                    step 21: 1763636908919537366
                    + 6637359198096363671
                    step 22: 8400996107015901037
                    + 7301095107016990048
                    step 23: 15702091214032891085
                    + 58019823041219020751
                    step 24: 73721914255251911836
                    + 63811915255241912737
                    step 25: 137533829510493824573
                    + 375428394015928335731
                    step 26: 512962223526422160304
                    + 403061224625322269215
                    step 27: 916023448151744429519
                    + 915924447151844320619
                    step 28: 1831947895303588750138
                    + 8310578853035987491381
                    step 29: 10142526748339576241519
                    + 91514267593384762524101
                    step 30: 101656794341724338765620
                    + 026567833427143497656101
                    step 31: 128224627768867836421721
                    + 127124638768867726422821
                    step 32: 255349266537735562844542
                    + 245448265537735662943552
                    step 33: 500797532075471225788094
                    + 490887522174570235797005
                    step 34: 991685054250041461585099
                    + 990585164140052450586199
                    step 35: 1982270218390093912171298
                    + 8921712193900938120722891
                    step 36: 10903982412291032032894189
                    + 98149823023019221428930901
                    step 37: 109053805435310253461825090
                    + 090528164352013534508350901
                    step 38: 199581969787323787970175991
                    + 199571079787323787969185991
                    step 39: 399153049574647575939361982
                    + 289163939575746475940351993
                    step 40: 688316989150394051879713975
                    + 579317978150493051989613886
                    step 41: 1267634967300887103869327861
                    + 1687239683017880037694367621
                    step 42: 2954874650318767141563695482
                    + 2845963651417678130564784592
                    step 43: 5800838301736445272128480074
                    + 4700848212725446371038380085
                    step 44: 10501686514461891643166860159
                    + 95106866134619816441568610501
                    step 45: 105608552649081708084735470660
                    + 066074537480807180946255806501
                    step 46: 171683090129888889030991277161
                    + 161772199030988888921090386171
                    step 47: 333455289160877777952081663332
                    + 233366180259777778061982554333
                    step 48: 566821469420655556014064217665
                    + 566712460410655556024964128665
                    step 49: 1133533929831311112039028346330
                    + 0336438209302111131389293353311
                    step 50: 1469972139133422243428321699641
                    + 1469961238243422243319312799641
                    step 51: 2939933377376844486747634499282
                    + 2829944367476844486737733399392
                    step 52: 5769877744853688973485367898674
                    + 4768987635843798863584477789675
                    step 53: 10538865380697487837069845688349
                    + 94388654896073878479608356883501
                    step 54: 104927520276771366316678202571850
                    + 058175202876613663177672025729401
                    step 55: 163102723153385029494350228301251
                    + 152103822053494920583351327201361
                    step 56: 315206545206879950077701555502612
                    + 216205555107770059978602545602513
                    step 57: 531412100314650010056304101105125
                    + 521501101403650010056413001214135
                    step 58: 1052913201718300020112717102319260
                    + 0629132017172110200038171023192501
                    step 59: 1682045218890410220150888125511761
                    + 1671155218880510220140988125402861
                    step 60: 3353200437770920440291876250914622
                    + 2264190526781920440290777340023533
                    step 61: 5617390964552840880582653590938155
                    + 5518390953562850880482554690937165
                    step 62: 11135781918115691761065208281875320
                    + 02357818280256016719651181918753111
                    step 63: 13493600198371708480716390200628431
                    + 13482600209361708480717389100639431
                    step 64: 26976200407733416961433779301267862
                    + 26876210397733416961433770400267962
                    step 65: 53852410805466833922867549701535824
                    + 42853510794576822933866450801425835
                    step 66: 96705921600043656856734000502961659
                    + 95616920500043765865634000612950769
                    step 67: 192322842100087422722368001115912428
                    + 824219511100863227224780001248223291
                    step 68: 1016542353200950649947148002364135719
                    + 9175314632008417499460590023532456101
                    step 69: 10191856985209368149407738025896591820
                    + 02819569852083770494186390258965819101
                    step 70: 13011426837293138643594128284862410921
                    + 12901426848282149534683139273862411031
                    step 71: 25912853685575288178277267558724821952
                    + 25912842785576277287188257558635821952
                    step 72: 51825696471151565465465525117360643904
                    + 40934606371152556456456515117469652815
                    step 73: 92760302842304121921922040234830296719
                    + 91769203843204022912912140324820306729
                    step 74: 184529506685508144834834180559650603448
                    + 844306056955081438438441805586605925481
                    step 75: 1028835563640589583273275986146256528929
                    + 9298256526416895723723859850463655388201
                    step 76: 10327092090057485306997135836609911917130
                    + 03171911990663853179960358475009029072301
                    step 77: 13499004080721338486957494311618940989431
                    + 13498904981611349475968483312708040099431
                    step 78: 26997909062332687962925977624326981088862
                    + 26888018962342677952926978623326090979962
                    step 79: 53885928024675365915852956247653072068824
                    + 42886027035674265925851956357642082958835
                    step 80: 96771955060349631841704912605295155027659
                    + 95672055159250621940714813694306055917769
                    step 81: 192444010219600253782419726299601210945428
                    + 824549012106992627914287352006912010444291
                    step 82: 1016993022326592881696707078306513221389719
                    + 9179831223156038707076961882956232203996101
                    step 83: 10196824245482631588773668961262745425385820
                    + 02858352454726216986637788513628454242869101
                    step 84: 13055176700208848575411457474891199668254921
                    + 12945286699119847475411457584880200767155031
                    step 85: 26000463399328696050822915059771400435409952
                    + 25990453400417795051922805069682399336400062
                    step 86: 51990916799746491102745720129453799771810014
                    + 41001817799735492102754720119464799761909915
                    step 87: 92992734599481983205500440248918599533719929
                    + 92991733599581984204400550238918499543729929
                    step 88: 185984468199063967409900990487837099077449858
                    + 858944770990738784099009904769360991864489581
                    step 89: 1044929239189802751508910895257198090941939439
                    + 9349391490908917525980198051572089819329294401
                    step 90: 10394320730098720277489108946829287910271233840
                    + 04833217201978292864980198477202789003702349301
                    step 91: 15227537932077013142469307424032076913973583141
                    + 14138537931967023042470396424131077023973572251
                    step 92: 29366075864044036184939703848163153937947155392
                    + 29355174973935136184830793948163044046857066392
                    step 93: 58721250837979172369770497796326197984804221784
                    + 48712240848979162369779407796327197973805212785
                    step 94: 107433491686958334739549905592653395958609434569
                    + 965434906859593356295509945937433859686194334701
                    step 95: 1072868398546551691035059851530087255644803769270
                    + 0729673084465527800351589505301961556458938682701
                    step 96: 1802541483012079491386649356832048812103742451971
                    + 1791542473012188402386539466831949702103841452081
                    step 97: 3594083956024267893773188823663998514207583904052
                    + 2504093857024158993663288813773987624206593804953
                    step 98: 6098177813048426887436477637437986138414177709005
                    + 5009077714148316897347367746347886248403187718906
                    step 99: 11107255527196743784783845383785872386817365427911
                    + 11972456371868327858738354838748734769172555270111
                    step 100: 23079711899065071643522200222534607155989920698022
                    + 22089602998955170643522200222534617056099811797032
                    step 101: 45169314898020242287044400445069224212089732495054
                    + 45059423798021242296054400444078224202089841396154
                    step 102: 90228738696041484583098800889147448414179573891208
                    + 80219837597141484474198800889038548414069683782209
                    step 103: 170448576293182969057297601778185996828249257673417
                    + 714376752942828699581877106792750969281392675844071
                    step 104: 884825329236011668639174708570936966109641933517488
                    + 884715339146901669639075807471936866110632923528488
                    step 105: 1769540668382913338278250516042873832220274857045976
                    + 6795407584720222383782406150528728333192838660459671
                    step 106: 8564948253103135722060656666571602165413113517505647
                    + 7465057153113145612061756666560602275313013528494658
                    step 107: 16030005406216281334122413333132204440726127046000305
                    + 50300064072162704440223133331422143318261260450003061
                    step 108: 66330069478378985774345546664554347758987387496003366
                    5020089949 takes 108 iterations / steps to resolve into a 53 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 2,095,949 times since Saturday, March 9th, 2002.)

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