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                    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 2,095,861 times since Saturday, March 9th, 2002.)

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