山水娱乐

  • REVERSAL-ADDITION PALINDROME TEST ON 1000007614641

    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 1000007614641:
    1000007614641
    + 1464167000001
    step 1: 2464174614642
    + 2464164714642
    step 2: 4928339329284
    + 4829239338294
    step 3: 9757578667578
    + 8757668757579
    step 4: 18515247425157
    + 75152474251581
    step 5: 93667721676738
    + 83767612776639
    step 6: 177435334453377
    + 773354433534771
    step 7: 950789767988148
    + 841889767987059
    step 8: 1792679535975207
    + 7025795359762971
    step 9: 8818474895738178
    + 8718375984748188
    step 10: 17536850880486366
    + 66368408805863571
    step 11: 83905259686349937
    + 73994368695250938
    step 12: 157899628381600875
    + 578006183826998751
    step 13: 735905812208599626
    + 626995802218509537
    step 14: 1362901614427109163
    + 3619017244161092631
    step 15: 4981918858588201794
    + 4971028858588191894
    step 16: 9952947717176393688
    + 8863936717177492599
    step 17: 18816884434353886287
    + 78268835343448861881
    step 18: 97085719777802748168
    + 86184720877791758079
    step 19: 183270440655594506247
    + 742605495556044072381
    step 20: 925875936211638578628
    + 826875836112639578529
    step 21: 1752751772324278157157
    + 7517518724232771572571
    step 22: 9270270496557049729728
    + 8279279407556940720729
    step 23: 17549549904113990450457
    + 75405409931140994594571
    step 24: 92954959835254985045028
    + 82054058945253895945929
    step 25: 175009018780508880990957
    + 759099088805087810900571
    step 26: 934108107585596691891528
    + 825198196695585701801439
    step 27: 1759306304281182393692967
    + 7692963932811824036039571
    step 28: 9452270237093006429732538
    + 8352379246003907320722549
    step 29: 17804649483096913750455087
    + 78055405731969038494640871
    step 30: 95860055215065952245095958
    + 85959054225956051255006859
    step 31: 181819109441022003500102817
    + 718201005300220144901918181
    step 32: 900020114741242148402020998
    + 899020204841242147411020009
    step 33: 1799040319582484295813041007
    + 7001403185924842859130409971
    step 34: 8800443505507327154943450978
    + 8790543494517237055053440088
    step 35: 17590987000024564209996891066
    + 66019869990246542000078909571
    step 36: 83610856990271106210075800637
    + 73600857001260117209965801638
    step 37: 157211713991531223420041602275
    + 572206140024322135199317112751
    step 38: 729417854015853358619358715026
    + 620517853916853358510458714927
    step 39: 1349935707932706717129817429953
    + 3599247189217176072397075399431
    step 40: 4949182897149882789526892829384
    + 4839282986259872889417982819494
    step 41: 9788465883409755678944875648878
    + 8788465784498765579043885648879
    step 42: 18576931667908521257988761297757
    + 75779216788975212580976613967581
    step 43: 94356148456883733838965375265338
    + 83356257356983833738865484165349
    step 44: 177712405813867567577830859430687
    + 786034958038775765768318504217771
    step 45: 963747363852643333346149363648458
    + 854846363941643333346258363747369
    step 46: 1818593727794286666692407727395827
    + 7285937277042966666824977273958181
    step 47: 9104531004837253333517385001354008
    + 8004531005837153333527384001354019
    step 48: 17109062010674406667044769002708027
    + 72080720096744076660447601026090171
    step 49: 89189782107418483327492370028798198
    + 89189782007329472338481470128798198
    step 50: 178379564114747955665973840157596396
    + 693695751048379566559747411465973871
    step 51: 872075315163127522225721251623570267
    + 762075326152127522225721361513570278
    step 52: 1634150641315255044451442613137140545
    + 5450417313162441544405525131460514361
    step 53: 7084567954477696588856967744597654906
    + 6094567954477696588856967744597654807
    step 54: 13179135908955393177713935489195309713
    + 31790359198453931777139355980953197131
    step 55: 44969495107409324954853291470148506844
    + 44860584107419235845942390470159496944
    step 56: 89830079214828560800795681940308003788
    + 88730080304918659700806582841297003898
    step 57: 178560159519747220501602264781605007686
    + 686700506187462206105022747915951065871
    step 58: 865260665707209426606625012697556073557
    + 755370655796210526606624902707566062568
    step 59: 1620631321503419953213249915405122136125
    + 5216312215045199423123599143051231360261
    step 60: 6836943536548619376336849058456353496386
    + 6836943536548509486336739168456353496386
    step 61: 13673887073097128862673588226912706992772
    + 27729960721962288537626882179037078837631
    step 62: 41403847795059417400300470405949785830403
    + 30403858794950407400300471495059774830414
    step 63: 71807706590009824800600941901009560660817
    + 71806606590010914900600842890009560770817
    step 64: 143614313180020739701201784791019121431634
    + 436134121910197487102107937020081313416341
    step 65: 579748435090218226803309721811100434847975
    + 579748434001118127903308622812090534847975
    step 66: 1159496869091336354706618344623190969695950
    + 0595969690913264438166074536331909686949511
    step 67: 1755466560004600792872692880955100656645461
    + 1645466560015590882962782970064000656645571
    step 68: 3400933120020191675835475851019101313291032
    + 2301923131019101585745385761910200213390043
    step 69: 5702856251039293261580861612929301526681075
    + 5701866251039292161680851623929301526582075
    step 70: 11404722502078585423261713236858603053263150
    + 05136235030685863231716232458587020522740411
    step 71: 16540957532764448654977945695445623576003561
    + 16530067532654459654977945684446723575904561
    step 72: 33071025065418908309955891379892347151908122
    + 22180915174329897319855990380981456052017033
    step 73: 55251940239748805629811881760873803203925155
    + 55152930230837806718811892650884793204915255
    step 74: 110404870470586612348623774411758596408840410
    + 014048804695857114477326843216685074078404011
    step 75: 124453675166443726825950617628443670487244421
    + 124442784076344826716059528627344661576354421
    step 76: 248896459242788553542010146255788332063598842
    + 248895360233887552641010245355887242954698842
    step 77: 497791819476676106183020391611675575018297684
    + 486792810575576116193020381601676674918197794
    step 78: 984584630052252222376040773213352249936495478
    + 874594639942253312377040673222252250036485489
    step 79: 1859179269994505534753081446435604499972980967
    + 7690892799944065346441803574355054999629719581
    step 80: 9550072069938570881194885020790659499602700548
    + 8450072069949560970205884911880758399602700559
    step 81: 18000144139888131851400769932671417899205401107
    + 70110450299871417623996700415813188893144100081
    step 82: 88110594439759549475397470348484606792349501188
    + 88110594329760648484307479357494595793449501188
    step 83: 176221188769520197959704949705979202585799002376
    + 673200997585202979507949407959791025967881122671
    step 84: 849422186354723177467654357665770228553680125047
    + 740521086355822077566753456764771327453681224948
    step 85: 1589943272710545255034407814430541556007361349995
    + 5999431637006551450344187044305525450172723499851
    step 86: 7589374909717096705378594858736067006180084849846
    + 6489484800816007606378584958735076907179094739857
    step 87: 14078859710533104311757179817471143913359179589703
    + 30798597195331934117471897175711340133501795887041
    step 88: 44877456905865038429229076993182484046860975476744
    + 44767457906864048428139967092292483056850965477844
    step 89: 89644914812729086857369044085474967103711940954588
    + 88545904911730176947458044096375868092721841944698
    step 90: 178190819724459263804827088181850835196433782899286
    + 682998287334691538058181880728408362954427918091871
    step 91: 861189107059150801863008968910259198150861700991157
    + 751199007168051891952019869800368108051950701981168
    step 92: 1612388114227202693815028838710627306202812402972325
    + 5232792042182026037260178388205183962027224118832161
    step 93: 6845180156409228731075207226915811268230036521804486
    + 6844081256300328621185196227025701378229046510815486
    step 94: 13689261412709557352260403453941512646459083032619972
    + 27991623038095464621514935430406225375590721416298631
    step 95: 41680884450805021973775338884347738022049804448918603
    + 30681984440894022083774348883357737912050805448808614
    step 96: 72362868891699044057549687767705475934100609897727217
    + 71272779890600143957450776778694575044099619886826327
    step 97: 143635648782299188015000464546400050978200229784553544
    + 445355487922002879050004645464000510881992287846536341
    step 98: 588991136704302067065005110010400561860192517631089885
    + 588980136715291068165004010011500560760203407631199885
    step 99: 1177971273419593135230009120021901122620395925262289770
    + 0779822625295930262211091200219000325313959143721797711
    step 100: 1957793898715523397441100320240901447934355068984087481
    + 1847804898605534397441090420230011447933255178983977591
    step 101: 3805598797321057794882190740470912895867610247968065072
    + 2705608697420167685982190740470912884977501237978955083
    step 102: 6511207494741225480864381480941825780845111485947020155
    + 5510207495841115480875281490841834680845221474947021156
    step 103: 12021414990582340961739662971783660461690332960894041311
    + 11314049806923309616406638717926693716904328509941412021
    step 104: 23335464797505650578146301689710354178594661470835453332
    + 23335453807416649587145301798610364187505650579746453332
    step 105: 46670918604922300165291603488320718366100312050581906664
    + 46660918505021300166381702388430619256100322940681907664
    step 106: 93331837109943600331673305876751337622200634991263814328
    + 82341836219943600222673315767850337613300634990173813339
    step 107: 175673673329887200554346621644601675235501269981437627667
    + 766726734189962105532576106446126643455002788923376376571
    step 108: 942400407519849306086922728090728318690504058904814004238
    + 832400418409850405096813827090827229680603948915704004249
    step 109: 1774800825929699711183736555181555548371108007820518008487
    + 7848008150287008011738455551815556373811179969295280084771
    step 110: 9622808976216707722922192106997111922182287977115798093258
    + 8523908975117797822812291117996012912292277076126798082269
    step 111: 18146717951334505545734483224993124834474565053242596175527
    + 72557169524235056547443842139942238443754550543315971764181
    step 112: 90703887475569562093178325364935363278229115596558567939708
    + 80793976585569551192287236353946352387139026596557478830709
    step 113: 171497864061139113285465561718881715665368142193116046770417
    + 714077640611391241863566517188817165564582311931160468794171
    step 114: 885575504672530355149032078907698881229950454124276515564588
    + 885465515672421454059922188896709870230941553035276405575588
    step 115: 1771041020344951809208954267804408751460892007159552921140176
    + 6710411292559517002980641578044087624598029081594430201401771
    step 116: 8481452312904468812189595845848496376058921088753983122541947
    + 7491452213893578801298506736948485485959812188644092132541848
    step 117: 15972904526798047613488102582796981862018733277398075255083795
    + 59738055257089377233781026818969728520188431674089762540927951
    step 118: 75710959783887424847269129401766710382207164951487837796011746
    + 64711069773878415946170228301766710492196274842478838795901757
    step 119: 140422029557765840793439357703533420874403439793966676591913503
    + 305319195676669397934304478024335307753934397048567755920224041
    step 120: 445741225234435238727743835727868728628337836842534432512137544
    + 445731215234435248638733826827868727538347727832534432522147544
    step 121: 891472440468870487366477662555737456166685564675068865034285088
    + 880582430568860576465586661654737555266774663784078864044274198
    step 122: 1772054871037731063832064324210475011433460228459147729078559286
    + 6829558709277419548220643341105740124234602383601377301784502771
    step 123: 8601613580315150612052707665316215135668062612060525030863062057
    + 7502603680305250602162608665315126135667072502160515130853161068
    step 124: 16104217260620401214215316330631341271335135114221040161716223125
    + 52132261716104012241153153317214313603361351241210402606271240161
    step 125: 68236478976724413455368469647845654874696486355431442767987463286
    1000007614641 takes 125 iterations / steps to resolve into a 65 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 2,061,597 times since Saturday, March 9th, 2002.)
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