山水娱乐

  • REVERSAL-ADDITION PALINDROME TEST ON 1008628

    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 1008628:
    1008628
    + 8268001
    step 1: 9276629
    + 9266729
    step 2: 18543358
    + 85334581
    step 3: 103877939
    + 939778301
    step 4: 1043656240
    + 0426563401
    step 5: 1470219641
    + 1469120741
    step 6: 2939340382
    + 2830439392
    step 7: 5769779774
    + 4779779675
    step 8: 10549559449
    + 94495594501
    step 9: 105045153950
    + 059351540501
    step 10: 164396694451
    + 154496693461
    step 11: 318893387912
    + 219783398813
    step 12: 538676786725
    + 527687676835
    step 13: 1066364463560
    + 0653644636601
    step 14: 1720009100161
    + 1610019000271
    step 15: 3330028100432
    + 2340018200333
    step 16: 5670046300765
    + 5670036400765
    step 17: 11340082701530
    + 03510728004311
    step 18: 14850810705841
    + 14850701805841
    step 19: 29701512511682
    + 28611521510792
    step 20: 58313034022474
    + 47422043031385
    step 21: 105735077053859
    + 958350770537501
    step 22: 1064085847591360
    + 0631957485804601
    step 23: 1696043333395961
    + 1695933333406961
    step 24: 3391976666802922
    + 2292086666791933
    step 25: 5684063333594855
    + 5584953333604865
    step 26: 11269016667199720
    + 02799176661096211
    step 27: 14068193328295931
    + 13959282339186041
    step 28: 28027475667481972
    + 27918476657472082
    step 29: 55945952324954054
    + 45045942325954955
    step 30: 100991894650909009
    + 900909056498199001
    step 31: 1001900951149108010
    + 0108019411590091001
    step 32: 1109920362739199011
    + 1109919372630299011
    step 33: 2219839735369498022
    + 2208949635379389122
    step 34: 4428789370748887144
    + 4417888470739878244
    step 35: 8846677841488765388
    + 8835678841487766488
    step 36: 17682356682976531876
    + 67813567928665328671
    step 37: 85495924611641860547
    + 74506814611642959458
    step 38: 160002739223284820005
    + 500028482322937200061
    step 39: 660031221546222020066
    + 660020222645122130066
    step 40: 1320051444191344150132
    + 2310514431914441500231
    step 41: 3630565876105785650363
    + 3630565875016785650363
    step 42: 7261131751122571300726
    + 6270031752211571311627
    step 43: 13531163503334142612353
    + 35321624143330536113531
    step 44: 48852787646664678725884
    1008628 takes 44 iterations / steps to resolve into a 23 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 2,061,761 times since Saturday, March 9th, 2002.)
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