山水娱乐

  • REVERSAL-ADDITION PALINDROME TEST ON 100055896

    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 100055896:
    100055896
    + 698550001
    step 1: 798605897
    + 798506897
    step 2: 1597112794
    + 4972117951
    step 3: 6569230745
    + 5470329656
    step 4: 12039560401
    + 10406593021
    step 5: 22446153422
    + 22435164422
    step 6: 44881317844
    + 44871318844
    step 7: 89752636688
    + 88663625798
    step 8: 178416262486
    + 684262614871
    step 9: 862678877357
    + 753778876268
    step 10: 1616457753625
    + 5263577546161
    step 11: 6880035299786
    + 6879925300886
    step 12: 13759960600672
    + 27600606995731
    step 13: 41360567596403
    + 30469576506314
    step 14: 71830144102717
    + 71720144103817
    step 15: 143550288206534
    + 435602882055341
    step 16: 579153170261875
    + 578162071351975
    step 17: 1157315241613850
    + 0583161425137511
    step 18: 1740476666751361
    + 1631576666740471
    step 19: 3372053333491832
    + 2381943333502733
    step 20: 5753996666994565
    + 5654996666993575
    step 21: 11408993333988140
    + 04188933339980411
    step 22: 15597926673968551
    + 15586937662979551
    step 23: 31184864336948102
    + 20184963346848113
    step 24: 51369827683796215
    + 51269738672896315
    step 25: 102639566356692530
    + 035296653665936201
    step 26: 137936220022628731
    + 137826220022639731
    step 27: 275762440045268462
    + 264862540044267572
    step 28: 540624980089536034
    + 430635980089426045
    step 29: 971260960178962079
    + 970269871069062179
    step 30: 1941530831248024258
    + 8524208421380351491
    step 31: 10465739252628375749
    + 94757382625293756401
    step 32: 105223121877922132150
    + 051231229778121322501
    step 33: 156454351656043454651
    + 156454340656153454651
    step 34: 312908692312196909302
    + 203909691213296809213
    step 35: 516818383525493718515
    + 515817394525383818615
    step 36: 1032635778050877537130
    + 0317357780508775362301
    step 37: 1349993558559652899431
    + 1349982569558553999431
    step 38: 2699976128118206898862
    + 2688986028118216799962
    step 39: 5388962156236423698824
    + 4288963246326512698835
    step 40: 9677925402562936397659
    + 9567936392652045297769
    step 41: 19245861795214981695428
    + 82459618941259716854291
    step 42: 101705480736474698549719
    + 917945896474637084507101
    step 43: 1019651377211111783056820
    + 0286503871111127731569101
    step 44: 1306155248322239514625921
    + 1295264159322238425516031
    step 45: 2601419407644477940141952
    + 2591410497744467049141062
    step 46: 5192829905388944989283014
    + 4103829894498835099282915
    step 47: 9296659799887780088565929
    + 9295658800877889979566929
    step 48: 18592318600765670068132858
    + 85823186007656700681329581
    step 49: 104415504608422370749462439
    + 934264947073224806405514401
    step 50: 1038680451681647177154976840
    + 0486794517717461861540868301
    step 51: 1525474969399109038695845141
    + 1415485968309019939694745251
    step 52: 2940960937708128978390590392
    + 2930950938798218077390690492
    step 53: 5871911876506347055781280884
    + 4880821875507436056781191785
    step 54: 10752733752013783112562472669
    + 96627426521138731025733725701
    step 55: 107380160273152514138296198370
    + 073891692831415251372061083701
    step 56: 181271853104567765510357282071
    + 170282753015567765401358172181
    step 57: 351554606120135530911715454252
    + 252454517119035531021606455153
    step 58: 604009123239171061933321909405
    + 504909123339160171932321900406
    step 59: 1108918246578331233865643809811
    + 1189083465683321338756428198011
    step 60: 2298001712261652572622072007822
    + 2287002702262752561622171008922
    step 61: 4585004414524405134244243016744
    + 4476103424424315044254144005854
    step 62: 9061107838948720178498387022598
    + 8952207838948710278498387011609
    step 63: 18013315677897430456996774034207
    + 70243047769965403479877651331081
    step 64: 88256363447862833936874425365288
    + 88256352447863933826874436365288
    step 65: 176512715895726767763748861730576
    + 675037168847367767627598517215671
    step 66: 851549884743094535391347378946247
    + 742649873743193535490347488945158
    step 67: 1594199758486288070881694867891405
    + 5041987684961880708826848579914951
    step 68: 6636187443448168779708543447806356
    + 6536087443458079778618443447816366
    step 69: 13172274886906248558326986895622722
    + 22722659868962385584260968847227131
    step 70: 35894934755868634142587955742849853
    + 35894824755978524143686855743949853
    step 71: 71789759511847158286274811486799706
    + 60799768411847268285174811595798717
    step 72: 132589527923694426571449623082598423
    + 324895280326944175624496329725985231
    step 73: 457484808250638602195945952808583654
    + 456385808259549591206836052808484754
    step 74: 913870616510188193402782005617068408
    + 804860716500287204391881015616078319
    step 75: 1718731333010475397794663021233146727
    + 7276413321203664977935740103331378171
    step 76: 8995144654214140375730403124564524898
    + 8984254654213040375730414124564415998
    step 77: 17979399308427180751460817249128940896
    + 69804982194271806415708172480399397971
    step 78: 87784381502698987167168989729528338867
    + 76883382592798986176178989620518348778
    step 79: 164667764095497973343347979350046687645
    + 546786640053979743343379794590467766461
    step 80: 711454404149477716686727773940514454106
    + 601454415049377727686617774941404454117
    step 81: 1312908819198855444373345548881918908223
    + 3228098191888455433734445588919188092131
    step 82: 4541007011087310878107791137801107000354
    + 4530007011087311977018780137801107001454
    step 83: 9071014022174622855126571275602214001808
    + 8081004122065721756215582264712204101709
    step 84: 17152018144240344611342153540314418103517
    + 71530181441304535124311644304244181025171
    step 85: 88682199585544879735653797844558599128688
    100055896 takes 85 iterations / steps to resolve into a 41 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 2,061,861 times since Saturday, March 9th, 2002.)
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