山水娱乐

  • REVERSAL-ADDITION PALINDROME TEST ON 10029826

    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 10029826:
    10029826
    + 62892001
    step 1: 72921827
    + 72812927
    step 2: 145734754
    + 457437541
    step 3: 603172295
    + 592271306
    step 4: 1195443601
    + 1063445911
    step 5: 2258889512
    + 2159888522
    step 6: 4418778034
    + 4308778144
    step 7: 8727556178
    + 8716557278
    step 8: 17444113456
    + 65431144471
    step 9: 82875257927
    + 72975257828
    step 10: 155850515755
    + 557515058551
    step 11: 713365574306
    + 603475563317
    step 12: 1316841137623
    + 3267311486131
    step 13: 4584152623754
    + 4573262514854
    step 14: 9157415138608
    + 8068315147519
    step 15: 17225730286127
    + 72168203752271
    step 16: 89393934038398
    + 89383043939398
    step 17: 178776977977796
    + 697779779677871
    step 18: 876556757655667
    + 766556757655678
    step 19: 1643113515311345
    + 5431135153113461
    step 20: 7074248668424806
    + 6084248668424707
    step 21: 13158497336849513
    + 31594863379485131
    step 22: 44753360716334644
    + 44643361706335744
    step 23: 89396722422670388
    + 88307622422769398
    step 24: 177704344845439786
    + 687934548443407771
    step 25: 865638893288847557
    + 755748882398836568
    step 26: 1621387775687684125
    + 5214867865777831261
    step 27: 6836255641465515386
    + 6835155641465526386
    step 28: 13671411282931041772
    + 27714013928211417631
    step 29: 41385425211142459403
    + 30495424111252458314
    step 30: 71880849322394917717
    + 71771949322394808817
    step 31: 143652798644789726534
    + 435627987446897256341
    step 32: 579280786091686982875
    + 578289686190687082975
    step 33: 1157570472282374065850
    + 0585604732822740757511
    step 34: 1743175205105114823361
    + 1633284115015025713471
    step 35: 3376459320120140536832
    + 2386350410210239546733
    step 36: 5762809730330380083565
    + 5653800830330379082675
    step 37: 11416610560660759166240
    + 04266195706606501661411
    step 38: 15682806267267260827651
    + 15672806276276260828651
    step 39: 31355612543543521656302
    + 20365612534534521655313
    step 40: 51721225078078043311615
    + 51611334087087052212715
    step 41: 103332559165165095524330
    + 033425590561561955233301
    step 42: 136758149726727050757631
    + 136757050727627941857631
    step 43: 273515200454354992615262
    + 262516299453454002515372
    step 44: 536031499907808995130634
    + 436031599808709994130635
    step 45: 972063099716518989261269
    + 962162989815617990360279
    step 46: 1934226089532136979621548
    + 8451269796312359806224391
    step 47: 10385495885844496785845939
    + 93954858769444858859458301
    step 48: 104340354655289355645304240
    + 042403546553982556453043401
    step 49: 146743901209271912098347641
    + 146743890219172902109347641
    step 50: 293487791428444814207695282
    + 282596702418444824197784392
    step 51: 576084493846889638405479674
    + 476974504836988648394480675
    step 52: 1053058998683878286799960349
    + 9430699976828783868998503501
    step 53: 10483758975512662155798463850
    + 05836489755126621557985738401
    step 54: 16320248730639283713784202251
    + 15220248731738293603784202361
    step 55: 31540497462377577317568404612
    + 21640486571377577326479404513
    step 56: 53180984033755154644047809125
    + 52190874044645155733048908135
    step 57: 105371858078400310377096717260
    + 062717690773013004870858173501
    step 58: 168089548851413315247954890761
    + 167098459742513314158845980861
    step 59: 335188008593926629406800871622
    + 226178008604926629395800881533
    step 60: 561366017198853258802601753155
    + 551357106208852358891710663165
    step 61: 1112723123407705617694312416320
    + 0236142134967165077043213272111
    step 62: 1348865258374870694737525688431
    + 1348865257374960784738525688431
    step 63: 2697730515749831479476051376862
    + 2686731506749741389475150377962
    step 64: 5384462022499572868951201754824
    + 4284571021598682759942202644835
    step 65: 9669033044098255628893404399659
    + 9569934043988265528904403309669
    step 66: 19238967088086521157797807709328
    + 82390770879775112568088076983291
    step 67: 101629737967861633725885884692619
    + 916296488588527336168769737926101
    step 68: 1017926226556388969894655622618720
    + 0278162265564989698836556226297101
    step 69: 1296088492121378668731211848915821
    + 1285198481121378668731212948806921
    step 70: 2581286973242757337462424797722742
    + 2472277974242647337572423796821852
    step 71: 5053564947485404675034848594544594
    + 4954454958484305764045847494653505
    step 72: 10008019905969710439080696089198099
    + 99089198069608093401796950991080001
    step 73: 109097217975577803840877647080278100
    + 001872080746778048308775579712790901
    step 74: 110969298722355852149653226793069001
    + 100960397622356941258553227892969011
    step 75: 211929696344712793408206454686038012
    + 210830686454602804397217443696929112
    step 76: 422760382799315597805423898382967124
    + 421769283898324508795513997283067224
    step 77: 844529666697640106600937895666034348
    + 843430666598739006601046796666925448
    step 78: 1687960333296379113201984692332959796
    + 6979592332964891023119736923330697861
    step 79: 8667552666261270136321721615663657657
    + 7567563665161271236310721626662557668
    step 80: 16235116331422541372632443242326215325
    + 52351262324234423627314522413361153261
    step 81: 68586378655656964999946965655687368586
    10029826 takes 81 iterations / steps to resolve into a 38 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 2,061,811 times since Saturday, March 9th, 2002.)
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