山水娱乐

  • REVERSAL-ADDITION PALINDROME TEST ON 190890

    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 190890:
    190890
    + 098091
    step 1: 288981
    + 189882
    step 2: 478863
    + 368874
    step 3: 847737
    + 737748
    step 4: 1585485
    + 5845851
    step 5: 7431336
    + 6331347
    step 6: 13762683
    + 38626731
    step 7: 52389414
    + 41498325
    step 8: 93887739
    + 93778839
    step 9: 187666578
    + 875666781
    step 10: 1063333359
    + 9533333601
    step 11: 10596666960
    + 06966669501
    step 12: 17563336461
    + 16463336571
    step 13: 34026673032
    + 23037662043
    step 14: 57064335075
    + 57053346075
    step 15: 114117681150
    + 051186711411
    step 16: 165304392561
    + 165293403561
    step 17: 330597796122
    + 221697795033
    step 18: 552295591155
    + 551195592255
    step 19: 1103491183410
    + 0143811943011
    step 20: 1247303126421
    + 1246213037421
    step 21: 2493516163842
    + 2483616153942
    step 22: 4977132317784
    + 4877132317794
    step 23: 9854264635578
    + 8755364624589
    step 24: 18609629260167
    + 76106292690681
    step 25: 94715921950848
    + 84805912951749
    step 26: 179521834902597
    + 795209438125971
    step 27: 974731273028568
    + 865820372137479
    step 28: 1840551645166047
    + 7406615461550481
    step 29: 9247167106716528
    + 8256176017617429
    step 30: 17503343124333957
    + 75933342134330571
    step 31: 93436685258664528
    + 82546685258663439
    step 32: 175983370517327967
    + 769723715073389571
    step 33: 945707085590717538
    + 835717095580707549
    step 34: 1781424181171425087
    + 7805241711814241871
    step 35: 9586665892985666958
    + 8596665892985666859
    step 36: 18183331785971333817
    + 71833317958713338181
    step 37: 90016649744684671998
    + 89917648644794661009
    step 38: 179934298389479333007
    + 700333974983892439971
    step 39: 880268273373371772978
    + 879277173373372862088
    step 40: 1759545446746744635066
    + 6605364476476445459571
    step 41: 8364909923223190094637
    + 7364900913223299094638
    step 42: 15729810836446489189275
    + 57298198464463801892751
    step 43: 73028009300910291082026
    + 62028019201900390082037
    step 44: 135056028502810681164063
    + 360461186018205820650531
    step 45: 495517214521016501814594
    + 495418105610125412715594
    step 46: 990935320131141914530188
    + 881035419141131023539099
    step 47: 1871970739272272938069287
    + 7829608392722729370791781
    step 48: 9701579131995002308861068
    + 8601688032005991319751079
    step 49: 18303267164000993628612147
    + 74121682639900046176230381
    step 50: 92424949803901039804842528
    + 82524840893010930894942429
    step 51: 174949790696911970699784957
    + 759487996079119696097949471
    step 52: 934437786776031666797734428
    + 824437797666130677687734439
    step 53: 1758875584442162344485468867
    + 7688645844432612444855788571
    step 54: 9447521428874774789341257438
    + 8347521439874774788241257449
    step 55: 17795042868749549577582514887
    + 78841528577594594786824059771
    step 56: 96636571446344144364406574658
    + 85647560446344144364417563669
    step 57: 182284131892688288728824138327
    + 723831428827882886298131482281
    step 58: 906115560720571175026955620608
    + 806026559620571175027065511609
    step 59: 1712142120341142350054021132217
    + 7122311204500532411430212412171
    step 60: 8834453324841674761484233544388
    190890 takes 60 iterations / steps to resolve into a 31 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 2,061,744 times since Saturday, March 9th, 2002.)
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