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                    REVERSAL-ADDITION PALINDROME TEST ON 100389898

                    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 100389898:
                    100389898
                    + 898983001
                    step 1: 999372899
                    + 998273999
                    step 2: 1997646898
                    + 8986467991
                    step 3: 10984114889
                    + 98841148901
                    step 4: 109825263790
                    + 097362528901
                    step 5: 207187792691
                    + 196297781702
                    step 6: 403485574393
                    + 393475584304
                    step 7: 796961158697
                    + 796851169697
                    step 8: 1593812328394
                    + 4938232183951
                    step 9: 6532044512345
                    + 5432154402356
                    step 10: 11964198914701
                    + 10741989146911
                    step 11: 22706188061612
                    + 21616088160722
                    step 12: 44322276222334
                    + 43322267222344
                    step 13: 87644543444678
                    + 87644434544678
                    step 14: 175288977989356
                    + 653989779882571
                    step 15: 829278757871927
                    + 729178757872928
                    step 16: 1558457515744855
                    + 5584475157548551
                    step 17: 7142932673293406
                    + 6043923762392417
                    step 18: 13186856435685823
                    + 32858653465868131
                    step 19: 46045509901553954
                    + 45935510990554064
                    step 20: 91981020892108018
                    + 81080129802018919
                    step 21: 173061150694126937
                    + 739621496051160371
                    step 22: 912682646745287308
                    + 803782547646286219
                    step 23: 1716465194391573527
                    + 7253751934915646171
                    step 24: 8970217129307219698
                    + 8969127039217120798
                    step 25: 17939344168524340496
                    + 69404342586144393971
                    step 26: 87343686754668734467
                    + 76443786645768634378
                    step 27: 163787473400437368845
                    + 548863734004374787361
                    step 28: 712651207404812156206
                    + 602651218404702156217
                    step 29: 1315302425809514312423
                    + 3242134159085242035131
                    step 30: 4557436584894756347554
                    + 4557436574984856347554
                    step 31: 9114873159879612695108
                    + 8015962169789513784119
                    step 32: 17130835329669126479227
                    + 72297462196692353803171
                    step 33: 89428297526361480282398
                    + 89328208416362579282498
                    step 34: 178756505942724059564896
                    + 698465950427249505657871
                    step 35: 877222456369973565222767
                    + 767222565379963654222778
                    step 36: 1644445021749937219445545
                    + 5455449127399471205444461
                    step 37: 7099894149149408424890006
                    + 6000984248049419414989907
                    step 38: 13100878397198827839879913
                    + 31997893872889179387800131
                    step 39: 45098772270088007227680044
                    + 44008672270088007227789054
                    step 40: 89107444540176014455469098
                    + 89096455441067104544470198
                    step 41: 178203899981243118999939296
                    + 692939999811342189998302871
                    step 42: 871143899792585308998242167
                    + 761242899803585297998341178
                    step 43: 1632386799596170606996583345
                    + 5433856996060716959976832361
                    step 44: 7066243795656887566973415706
                    + 6075143796657886565973426607
                    step 45: 13141387592314774132946842313
                    + 31324864923147741329578314131
                    step 46: 44466252515462515462525156444
                    + 44465152526451526451525266444
                    step 47: 88931405041914041914050422888
                    + 88822405041914041914050413988
                    step 48: 177753810083828083828100836876
                    + 678638001828380828380018357771
                    step 49: 856391811912208912208119194647
                    + 746491911802219802219118193658
                    step 50: 1602883723714428714427237388305
                    + 5038837327244178244173273882061
                    step 51: 6641721050958606958600511270366
                    + 6630721150068596068590501271466
                    step 52: 13272442201027203027191012541832
                    + 23814521019172030272010224427231
                    step 53: 37086963220199233299201236969063
                    + 36096963210299233299102236968073
                    step 54: 73183926430498466598303473937136
                    + 63173937430389566489403462938137
                    step 55: 136357863860888033087706936875273
                    + 372578639607780330888068368753631
                    step 56: 508936503468668363975775305628904
                    + 409826503577579363866864305639805
                    step 57: 918763007046247727842639611268709
                    + 907862116936248727742640700367819
                    step 58: 1826625123982496455585280311636528
                    + 8256361130825855546942893215266281
                    step 59: 10082986254808352002528173526902809
                    + 90820962537182520025380845268928001
                    step 60: 100903948791990872027909018795830810
                    + 018038597810909720278099197849309001
                    step 61: 118942546602900592306008216645139811
                    + 118931546612800603295009206645249811
                    step 62: 237874093215701195601017423290389622
                    + 226983092324710106591107512390478732
                    step 63: 464857185540411302192124935680868354
                    + 453868086539421291203114045581758464
                    step 64: 918725272079832593395238981262626818
                    + 818626262189832593395238970272527819
                    step 65: 1737351534269665186790477951535154637
                    + 7364515351597740976815669624351537371
                    step 66: 9101866885867406163606147575886692008
                    + 8002966885757416063616047685886681019
                    step 67: 17104833771624822227222195261773373027
                    + 72037337716259122272222842617733840171
                    step 68: 89142171487883944499445037879507213198
                    + 89131270597873054499444938878417124198
                    step 69: 178273442085756998998889976757924337396
                    + 693733429757679988899899657580244372871
                    step 70: 872006871843436987898789634338168710267
                    + 762017861833436987898789634348178600278
                    step 71: 1634024733676873975797579268686347310545
                    + 5450137436868629757975793786763374204361
                    step 72: 7084162170545503733773373055449721514906
                    + 6094151279445503733773373055450712614807
                    step 73: 13178313449991007467546746110900434129713
                    + 31792143400901164764576470019994431387131
                    step 74: 44970456850892172232123216130894865516844
                    + 44861556849803161232123227129805865407944
                    step 75: 89832013700695333464246443260700730924788
                    + 88742903700706234464246433359600731023898
                    step 76: 178574917401401567928492876620301461948686
                    + 686849164103026678294829765104104719475871
                    step 77: 865424081504428246223322641724406181424557
                    + 755424181604427146223322642824405180424568
                    step 78: 1620848263108855392446645284548811361849125
                    + 5219481631188454825466442935588013628480261
                    step 79: 6840329894297310217913088220136824990329386
                    + 6839230994286310228803197120137924989230486
                    step 80: 13679560888583620446716285340274749979559872
                    + 27895597994747204358261764402638588806597631
                    step 81: 41575158883330824804978049742913338786157503
                    + 30575168783331924794087940842803338885157514
                    step 82: 72150327666662749599065990585716677671315017
                    + 71051317677661758509956099594726666672305127
                    step 83: 143201645344324508109022090180443344343620144
                    + 441026343443344081090220901805423443546102341
                    step 84: 584227988787668589199242991985866787889722485
                    100389898 takes 84 iterations / steps to resolve into a 45 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 2,095,934 times since Saturday, March 9th, 2002.)

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