山水娱乐

  • REVERSAL-ADDITION PALINDROME TEST ON 7008429

    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 7008429:
    7008429
    + 9248007
    step 1: 16256436
    + 63465261
    step 2: 79721697
    + 79612797
    step 3: 159334494
    + 494433951
    step 4: 653768445
    + 544867356
    step 5: 1198635801
    + 1085368911
    step 6: 2284004712
    + 2174004822
    step 7: 4458009534
    + 4359008544
    step 8: 8817018078
    + 8708107188
    step 9: 17525125266
    + 66252152571
    step 10: 83777277837
    + 73877277738
    step 11: 157654555575
    + 575555456751
    step 12: 733210012326
    + 623210012337
    step 13: 1356420024663
    + 3664200246531
    step 14: 5020620271194
    + 4911720260205
    step 15: 9932340531399
    + 9931350432399
    step 16: 19863690963798
    + 89736909636891
    step 17: 109600600600689
    + 986006006006901
    step 18: 1095606606607590
    + 0957066066065901
    step 19: 2052672672673491
    + 1943762762762502
    step 20: 3996435435435993
    + 3995345345346993
    step 21: 7991780780782986
    + 6892870870871997
    step 22: 14884651651654983
    + 38945615615648841
    step 23: 53830267267303824
    + 42830376276203835
    step 24: 96660643543507659
    + 95670534534606669
    step 25: 192331178078114328
    + 823411870871133291
    step 26: 1015743048949247619
    + 9167429498403475101
    step 27: 10183172547352722720
    + 02722725374527138101
    step 28: 12905897921879860821
    + 12806897812979850921
    step 29: 25712795734859711742
    + 24711795843759721752
    step 30: 50424591578619433494
    + 49433491687519542405
    step 31: 99858083266138975899
    + 99857983166238085899
    step 32: 199716066432377061798
    + 897160773234660617991
    step 33: 1096876839667037679789
    + 9879767307669386786901
    step 34: 10976644147336424466690
    + 09666442463374144667901
    step 35: 20643086610710569134591
    + 19543196501701668034602
    step 36: 40186283112412237169193
    + 39196173221421138268104
    step 37: 79382456333833375437297
    + 79273457333833365428397
    step 38: 158655913667666740865694
    + 496568047666766319556851
    step 39: 655223961334433060422545
    + 545224060334433169322556
    step 40: 1200448021668866229745101
    + 1015479226688661208440021
    step 41: 2215927248357527438185122
    + 2215818347257538427295122
    step 42: 4431745595615065865480244
    + 4420845685605165955471344
    step 43: 8852591281220231820951588
    + 8851590281320221821952588
    step 44: 17704181562540453642904176
    + 67140924635404526518140771
    step 45: 84845106197944980161044947
    + 74944016108944979160154848
    step 46: 159789122306889959321199795
    + 597991123959988603221987951
    step 47: 757780246266878562543187746
    + 647781345265878662642087757
    step 48: 1405561591532757225185275503
    + 3055725815227572351951655041
    step 49: 4461287406760329577136930544
    + 4450396317759230676047821644
    step 50: 8911683724519560253184752188
    + 8812574813520659154273861198
    step 51: 17724258538040219407458613386
    + 68331685470491204083585242771
    step 52: 86055944008531423491043856157
    + 75165834019432413580044955068
    step 53: 161221778027963837071088811225
    + 522118880170738369720877122161
    step 54: 683340658198702206791965933386
    + 683339569197602207891856043386
    step 55: 1366680227396304414683821976772
    + 2776791283864144036937220866631
    step 56: 4143471511260448451621042843403
    + 3043482401261548440621151743414
    step 57: 7186953912521996892242194586817
    + 7186854912422986991252193596817
    step 58: 14373808824944983883494388183634
    + 43638188349438838944942880837341
    step 59: 58011997174383822828437269020975
    + 57902096273482822838347179911085
    step 60: 115914093447866645666784448932060
    + 060239844487666546668744390419511
    step 61: 176153937935533192335528839351571
    + 175153938825533291335539739351671
    step 62: 351307876761066483671068578703242
    + 242307875860176384660167678703153
    step 63: 593615752621242868331236257406395
    + 593604752632133868242126257516395
    step 64: 1187220505253376736573362514922790
    + 0972294152633756376733525050227811
    step 65: 2159514657887133113306887565150601
    + 1060515657886033113317887564159512
    step 66: 3220030315773166226624775129310113
    + 3110139215774266226613775130300223
    step 67: 6330169531547432453238550259610336
    + 6330169520558323542347451359610336
    step 68: 12660339052105755995586001619220672
    + 27602291610068559955750125093306621
    step 69: 40262630662174315951336126712527293
    + 39272521762163315951347126603626204
    step 70: 79535152424337631902683253316153497
    + 79435161335238620913673342425153597
    step 71: 158970313759576252816356595741307094
    + 490703147595653618252675957313079851
    step 72: 649673461355229871069032553054386945
    + 549683450355230960178922553164376946
    step 73: 1199356911710460831247955106218763891
    + 1983678126015597421380640171196539911
    step 74: 3183035037726058252628595277415303802
    + 2083035147725958262528506277305303813
    step 75: 5266070185452016515157101554720607615
    + 5167060274551017515156102545810706625
    step 76: 10433130460003034030313204100531314240
    + 04241313500140231303043030006403133401
    step 77: 14674443960143265333356234106934447641
    7008429 takes 77 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 2,061,798 times since Saturday, March 9th, 2002.)
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