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                    REVERSAL-ADDITION PALINDROME TEST ON 16207990

                    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 16207990:
                    16207990
                    + 09970261
                    step 1: 26178251
                    + 15287162
                    step 2: 41465413
                    + 31456414
                    step 3: 72921827
                    + 72812927
                    step 4: 145734754
                    + 457437541
                    step 5: 603172295
                    + 592271306
                    step 6: 1195443601
                    + 1063445911
                    step 7: 2258889512
                    + 2159888522
                    step 8: 4418778034
                    + 4308778144
                    step 9: 8727556178
                    + 8716557278
                    step 10: 17444113456
                    + 65431144471
                    step 11: 82875257927
                    + 72975257828
                    step 12: 155850515755
                    + 557515058551
                    step 13: 713365574306
                    + 603475563317
                    step 14: 1316841137623
                    + 3267311486131
                    step 15: 4584152623754
                    + 4573262514854
                    step 16: 9157415138608
                    + 8068315147519
                    step 17: 17225730286127
                    + 72168203752271
                    step 18: 89393934038398
                    + 89383043939398
                    step 19: 178776977977796
                    + 697779779677871
                    step 20: 876556757655667
                    + 766556757655678
                    step 21: 1643113515311345
                    + 5431135153113461
                    step 22: 7074248668424806
                    + 6084248668424707
                    step 23: 13158497336849513
                    + 31594863379485131
                    step 24: 44753360716334644
                    + 44643361706335744
                    step 25: 89396722422670388
                    + 88307622422769398
                    step 26: 177704344845439786
                    + 687934548443407771
                    step 27: 865638893288847557
                    + 755748882398836568
                    step 28: 1621387775687684125
                    + 5214867865777831261
                    step 29: 6836255641465515386
                    + 6835155641465526386
                    step 30: 13671411282931041772
                    + 27714013928211417631
                    step 31: 41385425211142459403
                    + 30495424111252458314
                    step 32: 71880849322394917717
                    + 71771949322394808817
                    step 33: 143652798644789726534
                    + 435627987446897256341
                    step 34: 579280786091686982875
                    + 578289686190687082975
                    step 35: 1157570472282374065850
                    + 0585604732822740757511
                    step 36: 1743175205105114823361
                    + 1633284115015025713471
                    step 37: 3376459320120140536832
                    + 2386350410210239546733
                    step 38: 5762809730330380083565
                    + 5653800830330379082675
                    step 39: 11416610560660759166240
                    + 04266195706606501661411
                    step 40: 15682806267267260827651
                    + 15672806276276260828651
                    step 41: 31355612543543521656302
                    + 20365612534534521655313
                    step 42: 51721225078078043311615
                    + 51611334087087052212715
                    step 43: 103332559165165095524330
                    + 033425590561561955233301
                    step 44: 136758149726727050757631
                    + 136757050727627941857631
                    step 45: 273515200454354992615262
                    + 262516299453454002515372
                    step 46: 536031499907808995130634
                    + 436031599808709994130635
                    step 47: 972063099716518989261269
                    + 962162989815617990360279
                    step 48: 1934226089532136979621548
                    + 8451269796312359806224391
                    step 49: 10385495885844496785845939
                    + 93954858769444858859458301
                    step 50: 104340354655289355645304240
                    + 042403546553982556453043401
                    step 51: 146743901209271912098347641
                    + 146743890219172902109347641
                    step 52: 293487791428444814207695282
                    + 282596702418444824197784392
                    step 53: 576084493846889638405479674
                    + 476974504836988648394480675
                    step 54: 1053058998683878286799960349
                    + 9430699976828783868998503501
                    step 55: 10483758975512662155798463850
                    + 05836489755126621557985738401
                    step 56: 16320248730639283713784202251
                    + 15220248731738293603784202361
                    step 57: 31540497462377577317568404612
                    + 21640486571377577326479404513
                    step 58: 53180984033755154644047809125
                    + 52190874044645155733048908135
                    step 59: 105371858078400310377096717260
                    + 062717690773013004870858173501
                    step 60: 168089548851413315247954890761
                    + 167098459742513314158845980861
                    step 61: 335188008593926629406800871622
                    + 226178008604926629395800881533
                    step 62: 561366017198853258802601753155
                    + 551357106208852358891710663165
                    step 63: 1112723123407705617694312416320
                    + 0236142134967165077043213272111
                    step 64: 1348865258374870694737525688431
                    + 1348865257374960784738525688431
                    step 65: 2697730515749831479476051376862
                    + 2686731506749741389475150377962
                    step 66: 5384462022499572868951201754824
                    + 4284571021598682759942202644835
                    step 67: 9669033044098255628893404399659
                    + 9569934043988265528904403309669
                    step 68: 19238967088086521157797807709328
                    + 82390770879775112568088076983291
                    step 69: 101629737967861633725885884692619
                    + 916296488588527336168769737926101
                    step 70: 1017926226556388969894655622618720
                    + 0278162265564989698836556226297101
                    step 71: 1296088492121378668731211848915821
                    + 1285198481121378668731212948806921
                    step 72: 2581286973242757337462424797722742
                    + 2472277974242647337572423796821852
                    step 73: 5053564947485404675034848594544594
                    + 4954454958484305764045847494653505
                    step 74: 10008019905969710439080696089198099
                    + 99089198069608093401796950991080001
                    step 75: 109097217975577803840877647080278100
                    + 001872080746778048308775579712790901
                    step 76: 110969298722355852149653226793069001
                    + 100960397622356941258553227892969011
                    step 77: 211929696344712793408206454686038012
                    + 210830686454602804397217443696929112
                    step 78: 422760382799315597805423898382967124
                    + 421769283898324508795513997283067224
                    step 79: 844529666697640106600937895666034348
                    + 843430666598739006601046796666925448
                    step 80: 1687960333296379113201984692332959796
                    + 6979592332964891023119736923330697861
                    step 81: 8667552666261270136321721615663657657
                    + 7567563665161271236310721626662557668
                    step 82: 16235116331422541372632443242326215325
                    + 52351262324234423627314522413361153261
                    step 83: 68586378655656964999946965655687368586
                    16207990 takes 83 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 2,095,930 times since Saturday, March 9th, 2002.)

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