山水娱乐

  • REVERSAL-ADDITION PALINDROME TEST ON 1017501

    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 1017501:
    1017501
    + 1057101
    step 1: 2074602
    + 2064702
    step 2: 4139304
    + 4039314
    step 3: 8178618
    + 8168718
    step 4: 16347336
    + 63374361
    step 5: 79721697
    + 79612797
    step 6: 159334494
    + 494433951
    step 7: 653768445
    + 544867356
    step 8: 1198635801
    + 1085368911
    step 9: 2284004712
    + 2174004822
    step 10: 4458009534
    + 4359008544
    step 11: 8817018078
    + 8708107188
    step 12: 17525125266
    + 66252152571
    step 13: 83777277837
    + 73877277738
    step 14: 157654555575
    + 575555456751
    step 15: 733210012326
    + 623210012337
    step 16: 1356420024663
    + 3664200246531
    step 17: 5020620271194
    + 4911720260205
    step 18: 9932340531399
    + 9931350432399
    step 19: 19863690963798
    + 89736909636891
    step 20: 109600600600689
    + 986006006006901
    step 21: 1095606606607590
    + 0957066066065901
    step 22: 2052672672673491
    + 1943762762762502
    step 23: 3996435435435993
    + 3995345345346993
    step 24: 7991780780782986
    + 6892870870871997
    step 25: 14884651651654983
    + 38945615615648841
    step 26: 53830267267303824
    + 42830376276203835
    step 27: 96660643543507659
    + 95670534534606669
    step 28: 192331178078114328
    + 823411870871133291
    step 29: 1015743048949247619
    + 9167429498403475101
    step 30: 10183172547352722720
    + 02722725374527138101
    step 31: 12905897921879860821
    + 12806897812979850921
    step 32: 25712795734859711742
    + 24711795843759721752
    step 33: 50424591578619433494
    + 49433491687519542405
    step 34: 99858083266138975899
    + 99857983166238085899
    step 35: 199716066432377061798
    + 897160773234660617991
    step 36: 1096876839667037679789
    + 9879767307669386786901
    step 37: 10976644147336424466690
    + 09666442463374144667901
    step 38: 20643086610710569134591
    + 19543196501701668034602
    step 39: 40186283112412237169193
    + 39196173221421138268104
    step 40: 79382456333833375437297
    + 79273457333833365428397
    step 41: 158655913667666740865694
    + 496568047666766319556851
    step 42: 655223961334433060422545
    + 545224060334433169322556
    step 43: 1200448021668866229745101
    + 1015479226688661208440021
    step 44: 2215927248357527438185122
    + 2215818347257538427295122
    step 45: 4431745595615065865480244
    + 4420845685605165955471344
    step 46: 8852591281220231820951588
    + 8851590281320221821952588
    step 47: 17704181562540453642904176
    + 67140924635404526518140771
    step 48: 84845106197944980161044947
    + 74944016108944979160154848
    step 49: 159789122306889959321199795
    + 597991123959988603221987951
    step 50: 757780246266878562543187746
    + 647781345265878662642087757
    step 51: 1405561591532757225185275503
    + 3055725815227572351951655041
    step 52: 4461287406760329577136930544
    + 4450396317759230676047821644
    step 53: 8911683724519560253184752188
    + 8812574813520659154273861198
    step 54: 17724258538040219407458613386
    + 68331685470491204083585242771
    step 55: 86055944008531423491043856157
    + 75165834019432413580044955068
    step 56: 161221778027963837071088811225
    + 522118880170738369720877122161
    step 57: 683340658198702206791965933386
    + 683339569197602207891856043386
    step 58: 1366680227396304414683821976772
    + 2776791283864144036937220866631
    step 59: 4143471511260448451621042843403
    + 3043482401261548440621151743414
    step 60: 7186953912521996892242194586817
    + 7186854912422986991252193596817
    step 61: 14373808824944983883494388183634
    + 43638188349438838944942880837341
    step 62: 58011997174383822828437269020975
    + 57902096273482822838347179911085
    step 63: 115914093447866645666784448932060
    + 060239844487666546668744390419511
    step 64: 176153937935533192335528839351571
    + 175153938825533291335539739351671
    step 65: 351307876761066483671068578703242
    + 242307875860176384660167678703153
    step 66: 593615752621242868331236257406395
    + 593604752632133868242126257516395
    step 67: 1187220505253376736573362514922790
    + 0972294152633756376733525050227811
    step 68: 2159514657887133113306887565150601
    + 1060515657886033113317887564159512
    step 69: 3220030315773166226624775129310113
    + 3110139215774266226613775130300223
    step 70: 6330169531547432453238550259610336
    + 6330169520558323542347451359610336
    step 71: 12660339052105755995586001619220672
    + 27602291610068559955750125093306621
    step 72: 40262630662174315951336126712527293
    + 39272521762163315951347126603626204
    step 73: 79535152424337631902683253316153497
    + 79435161335238620913673342425153597
    step 74: 158970313759576252816356595741307094
    + 490703147595653618252675957313079851
    step 75: 649673461355229871069032553054386945
    + 549683450355230960178922553164376946
    step 76: 1199356911710460831247955106218763891
    + 1983678126015597421380640171196539911
    step 77: 3183035037726058252628595277415303802
    + 2083035147725958262528506277305303813
    step 78: 5266070185452016515157101554720607615
    + 5167060274551017515156102545810706625
    step 79: 10433130460003034030313204100531314240
    + 04241313500140231303043030006403133401
    step 80: 14674443960143265333356234106934447641
    1017501 takes 80 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 2,061,646 times since Saturday, March 9th, 2002.)
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