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                    REVERSAL-ADDITION PALINDROME TEST ON 178992

                    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 178992:
                    178992
                    + 299871
                    step 1: 478863
                    + 368874
                    step 2: 847737
                    + 737748
                    step 3: 1585485
                    + 5845851
                    step 4: 7431336
                    + 6331347
                    step 5: 13762683
                    + 38626731
                    step 6: 52389414
                    + 41498325
                    step 7: 93887739
                    + 93778839
                    step 8: 187666578
                    + 875666781
                    step 9: 1063333359
                    + 9533333601
                    step 10: 10596666960
                    + 06966669501
                    step 11: 17563336461
                    + 16463336571
                    step 12: 34026673032
                    + 23037662043
                    step 13: 57064335075
                    + 57053346075
                    step 14: 114117681150
                    + 051186711411
                    step 15: 165304392561
                    + 165293403561
                    step 16: 330597796122
                    + 221697795033
                    step 17: 552295591155
                    + 551195592255
                    step 18: 1103491183410
                    + 0143811943011
                    step 19: 1247303126421
                    + 1246213037421
                    step 20: 2493516163842
                    + 2483616153942
                    step 21: 4977132317784
                    + 4877132317794
                    step 22: 9854264635578
                    + 8755364624589
                    step 23: 18609629260167
                    + 76106292690681
                    step 24: 94715921950848
                    + 84805912951749
                    step 25: 179521834902597
                    + 795209438125971
                    step 26: 974731273028568
                    + 865820372137479
                    step 27: 1840551645166047
                    + 7406615461550481
                    step 28: 9247167106716528
                    + 8256176017617429
                    step 29: 17503343124333957
                    + 75933342134330571
                    step 30: 93436685258664528
                    + 82546685258663439
                    step 31: 175983370517327967
                    + 769723715073389571
                    step 32: 945707085590717538
                    + 835717095580707549
                    step 33: 1781424181171425087
                    + 7805241711814241871
                    step 34: 9586665892985666958
                    + 8596665892985666859
                    step 35: 18183331785971333817
                    + 71833317958713338181
                    step 36: 90016649744684671998
                    + 89917648644794661009
                    step 37: 179934298389479333007
                    + 700333974983892439971
                    step 38: 880268273373371772978
                    + 879277173373372862088
                    step 39: 1759545446746744635066
                    + 6605364476476445459571
                    step 40: 8364909923223190094637
                    + 7364900913223299094638
                    step 41: 15729810836446489189275
                    + 57298198464463801892751
                    step 42: 73028009300910291082026
                    + 62028019201900390082037
                    step 43: 135056028502810681164063
                    + 360461186018205820650531
                    step 44: 495517214521016501814594
                    + 495418105610125412715594
                    step 45: 990935320131141914530188
                    + 881035419141131023539099
                    step 46: 1871970739272272938069287
                    + 7829608392722729370791781
                    step 47: 9701579131995002308861068
                    + 8601688032005991319751079
                    step 48: 18303267164000993628612147
                    + 74121682639900046176230381
                    step 49: 92424949803901039804842528
                    + 82524840893010930894942429
                    step 50: 174949790696911970699784957
                    + 759487996079119696097949471
                    step 51: 934437786776031666797734428
                    + 824437797666130677687734439
                    step 52: 1758875584442162344485468867
                    + 7688645844432612444855788571
                    step 53: 9447521428874774789341257438
                    + 8347521439874774788241257449
                    step 54: 17795042868749549577582514887
                    + 78841528577594594786824059771
                    step 55: 96636571446344144364406574658
                    + 85647560446344144364417563669
                    step 56: 182284131892688288728824138327
                    + 723831428827882886298131482281
                    step 57: 906115560720571175026955620608
                    + 806026559620571175027065511609
                    step 58: 1712142120341142350054021132217
                    + 7122311204500532411430212412171
                    step 59: 8834453324841674761484233544388
                    178992 takes 59 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 2,095,858 times since Saturday, March 9th, 2002.)

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