山水娱乐

  • 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 2,061,816 times since Saturday, March 9th, 2002.)
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