|
REVERSAL-ADDITION
PALINDROME
TEST ON
1631002019993
|
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 1631002019993: |
1631002019993
+ 3999102001361
step 1: 5630104021354
+ 4531204010365
step 2: 10161308031719
+ 91713080316101
step 3: 101874388347820
+ 028743883478101
step 4: 130618271825921
+ 129528172816031
step 5: 260146444641952
+ 259146444641062
step 6: 519292889283014
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step 7: 929675877575929
+ 929575778576929
step 8: 1859251656152858
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step 9: 10441768217682439
+ 93428671286714401
step 10: 103870439504396840
+ 048693405934078301
step 11: 152563845438475141
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step 12: 294138679986840392
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step 13: 587187369963671884
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step 14: 1075363739927453669
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step 15: 10738911039301089370
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step 16: 18136921432313073071
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step 17: 35173952755726036252
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step 18: 60437015511451973405
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step 19: 110874930923003046811
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step 20: 229515231252042524822
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step 21: 457940471504175040744
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step 22: 904981042909349090498
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step 23: 1799071986818589279907
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step 24: 8898801845005480989878
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step 25: 17688692690010962078866
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step 26: 84575719591020591767537
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step 74: 88262010245569727604949572796554311015288
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step 75: 176513021591139455199890245593108512041576
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step 76: 851653237392534997298881800524303632357247
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step 77: 1594406473695960005487774599959597364713405
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step 78: 6637581111655559960265619600655561110758356
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step 79: 13176151223311120029431240300211122222615722
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step 80: 35927773445422320333644732302322454437782853
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step 81: 71756546890844640657389365604644908875555806
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step 82: 132612104771789281313787741209289718740121523
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step 83: 457733152589772183461575054392276896141337754
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step 84: 915466294288444476912150218773554881392675508
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step 85: 1721042587476899854724201438447999763885340027
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step 86: 8921478471156897303065225713037986511737741298
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step 87: 17842955842313794606240451316075973023486482596
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step 88: 87371424274351751667555855576725704348342407467
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step 89: 163841848658692504435111711153341419695584824845
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step 90: 712270334255606647786228822687746716552432973206
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step 91: 1314649568511224295572457645375493323104866045423
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step 92: 4560056252524458241307925188131417544263525509554
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step 93: 9119111506148915382626740485162846088516052010208
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step 94: 17139214012307721865242580961425681286932103129327
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step 95: 89531344136275940517659489485682494057253144422498
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step 96: 178953788271550989946317987981353999014516288736096
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step 97: 869591670886961989299507777695003988069689176095967
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step 98: 1639182342873922878600104555400996977239377252291935
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step 99: 7031104870613250675590150109411065759533159685111296
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step 100: 13952220740126610251191299119922021520056320469122603
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step 101: 44574417142491612763214290319141136721718425171348534
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step 102: 88158734294973325526328481628382373443337849342796078
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step 103: 175228458689846659963656864246864735995675798586581266
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step 104: 837414144587423259501125506715521105952324785441403837
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step 105: 1575718289174846519002251024321042211904649570882818575
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step 106: 7333901169934310610124652258522564221061134290710994326
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step 107: 13568891340858622211349304517045128431221268690322087663
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step 108: 50246913650544834424831458588585522742443954494641974194
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step 109: 99394828299990768849554017177170936584887799000273938399
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step 110: 198778765500090547698117924354341982179774508999556787798
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step 111: 1096566421499896025669407067807771694076519599005124665689
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step 112: 10962230636509855182374368844895378743741726588946371322590
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step 113: 20484548001498417897109156204740265091069882479509974549491
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step 135: 13712010365863952926161109273168488957514819110615302503595531202172
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step 139: 567037730387675932232751117276345809643671720156232240675694037729665
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step 141: 1474611168626772819108533488890510891149888843359109271777357721153741
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step 146: 159925636346599089247437690625523294491225626086843643089895643647518951
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step 157: 604345630446817178842362258765973514526514280657853164237882608753927534495
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step 158: 1198781359804623467574823617522055930151929660225705427486754327397964077901
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step 159: 2296486057741858044422068692742725221662325162482868712244397591487495956812
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step 160: 4483082005583815978844247375585340454323550434955837314488806172965002803734
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step 161: 8856164011276532067688384761179681007558090870811574738977601356820005607578
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step 162: 17613229011563063135486759512360461916115092740523249577845203713541110224166
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step 163: 83755430126094793390364353744865190967277009146844845346298339750052202455837
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step 164: 157610850351100586779628708589729381044553918303689580692607679499114305911575
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step 165: 732730353763095563485924794576033200399994102231675388519585364500267363928326
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step 166: 1356559717525101027071840678152165401899987104562350885949169730090634716965563
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step 167: 5012255891886001406691336558684819419799968150174869646430876931105891896522094
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step 168: 9914512873871012803471683028369529938499947299359738202762842972112773882044199
+ 9914402883772112792482672028379539927499948399259638203861743082101783782154199
step 169: 19828915757643125595954355056749069865999895698619376406624586054214557664198398
+ 89389146675541245068542660467391689659899956896094765055345959552134675751982891
step 170: 109218062433184370664497015524140759525899852594714141461970545606349233416181289
+ 982181614332943606545079164141417495258998525957041425510794466073481334260812901
step 171: 1091399676766127977209576179665558254784898378551755566972765011679830567676994190
+ 0914996767650389761105672796655571558738984874528555669716759027797216676769931901
step 172: 2006396444416517738315248976321129813523883253080311236689524039477047244446926091
+ 1906296444427407749304259866321130803523883253189211236798425138377156144446936002
step 173: 3912692888843925487619508842642260617047766506269522473487949177854203388893862093
+ 3902683988833024587719497843742259626056677407160622462488059167845293488882962193
step 174: 7815376877676950075339006686384520243104443913430144935976008345699496877776824286
+ 6824286777786949965438006795394410343193444013420254836866009335700596767786735187
step 175: 14639663655463900040777013481778930586297887926850399772842017681400093645563559473
+ 37495536554639000418671024827799305862978879268503987718431077704000936455636693641
step 176: 52135200210102900459448038309578236449276767195354387491273095385401030101200253114
+ 41135200210103010458359037219478345359176767294463287590383084495400920101200253125
step 177: 93270400420205910917807075529056581808453534489817675081656179880801950202400506239
+ 93260500420205910808897165618057671898443535480818565092557070871901950202400407239
step 178: 186530900840411821726704241147114253706897069970636240174213250752703900404800913478
+ 874319008404009307257052312471042636079960798607352411741142407627128114048009035681
step 179: 1060849909244421128983756553618156889786857868577988651915355658379832014452809949159
+ 9519499082544102389738565535191568897758687586879886518163556573898211244429099480601
step 180: 10580348991788523518722322088809725787545545455457875170078912232278043258881909429760
+ 06792490918885234087223221987007157875455454554578752790888022322781532588719984308501
step 181: 17372839910673757605945544075816883663001000010036627960966934555059575847601893738261
+ 16283739810674857595055543966906972663001000010036638861857044554950675737601993827371
step 182: 33656579721348615201001088042723856326002000020073266822823979110010251585203887565632
+ 23656578830258515201001197932822866237002000020062365832724088010010251684312797565633
step 183: 57313158551607130402002285975546722563004000040135632655548067120020503269516685131265
+ 56213158661596230502002176084555623653104000040036522764557958220020403170615585131375
step 184: 113526317213203360904004462060102346216108000080172155420106025340040906440132270262640
+ 046262072231044609040043520601024551271080000801612643201060264400409063302312713625311
step 185: 159788389444247969944047982661126897487188000881784798621166289740449969742444983887951
|
|
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1631002019993 takes 185 iterations / steps to resolve into a 87 digit palindrome.
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REVERSAL-ADDITION
PALINDROME
RECORDS
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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.)
| Digits | Number | Result |
|---|
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!
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| [View all records] |
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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 2,542,573 times since Saturday, March 9th, 2002.)
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