|
REVERSAL-ADDITION
PALINDROME
TEST ON
1600402195090
|
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 1600402195090: |
1600402195090
+ 0905912040061
step 1: 2506314235151
+ 1515324136052
step 2: 4021638371203
+ 3021738361204
step 3: 7043376732407
+ 7042376733407
step 4: 14085753465814
+ 41856435758041
step 5: 55942189223855
+ 55832298124955
step 6: 111774487348810
+ 018843784477111
step 7: 130618271825921
+ 129528172816031
step 8: 260146444641952
+ 259146444641062
step 9: 519292889283014
+ 410382988292915
step 10: 929675877575929
+ 929575778576929
step 11: 1859251656152858
+ 8582516561529581
step 12: 10441768217682439
+ 93428671286714401
step 13: 103870439504396840
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step 14: 152563845438475141
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step 15: 294138679986840392
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step 16: 587187369963671884
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step 17: 1075363739927453669
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step 18: 10738911039301089370
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step 19: 18136921432313073071
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step 20: 35173952755726036252
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step 21: 60437015511451973405
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step 22: 110874930923003046811
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step 23: 229515231252042524822
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step 24: 457940471504175040744
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step 25: 904981042909349090498
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step 26: 1799071986818589279907
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step 27: 8898801845005480989878
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step 28: 17688692690010962078866
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step 30: 158152439093040183525085
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step 32: 1378355531267762146553773
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step 33: 5151911943945383502092504
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step 34: 9204813997780876993284019
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step 35: 18309637994561754986468048
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step 72: 177930819051424747088074642315091912887
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step 76: 17122819114134611599450061153413119193117
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step 77: 88262010245569727604949572796554311015288
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step 78: 176513021591139455199890245593108512041576
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step 79: 851653237392534997298881800524303632357247
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step 80: 1594406473695960005487774599959597364713405
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step 81: 6637581111655559960265619600655561110758356
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step 82: 13176151223311120029431240300211122222615722
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step 83: 35927773445422320333644732302322454437782853
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step 84: 71756546890844640657389365604644908875555806
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step 85: 132612104771789281313787741209289718740121523
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step 86: 457733152589772183461575054392276896141337754
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step 87: 915466294288444476912150218773554881392675508
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step 88: 1721042587476899854724201438447999763885340027
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step 89: 8921478471156897303065225713037986511737741298
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step 90: 17842955842313794606240451316075973023486482596
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step 91: 87371424274351751667555855576725704348342407467
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step 92: 163841848658692504435111711153341419695584824845
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step 93: 712270334255606647786228822687746716552432973206
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step 94: 1314649568511224295572457645375493323104866045423
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step 95: 4560056252524458241307925188131417544263525509554
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step 96: 9119111506148915382626740485162846088516052010208
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step 97: 17139214012307721865242580961425681286932103129327
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step 98: 89531344136275940517659489485682494057253144422498
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step 99: 178953788271550989946317987981353999014516288736096
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step 100: 869591670886961989299507777695003988069689176095967
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step 101: 1639182342873922878600104555400996977239377252291935
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step 102: 7031104870613250675590150109411065759533159685111296
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step 103: 13952220740126610251191299119922021520056320469122603
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step 104: 44574417142491612763214290319141136721718425171348534
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step 105: 88158734294973325526328481628382373443337849342796078
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step 106: 175228458689846659963656864246864735995675798586581266
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step 107: 837414144587423259501125506715521105952324785441403837
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step 108: 1575718289174846519002251024321042211904649570882818575
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step 109: 7333901169934310610124652258522564221061134290710994326
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step 110: 13568891340858622211349304517045128431221268690322087663
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step 111: 50246913650544834424831458588585522742443954494641974194
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step 112: 99394828299990768849554017177170936584887799000273938399
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step 113: 198778765500090547698117924354341982179774508999556787798
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step 114: 1096566421499896025669407067807771694076519599005124665689
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step 115: 10962230636509855182374368844895378743741726588946371322590
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step 116: 20484548001498417897109156204740265091069882479509974549491
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step 117: 39979095992095846793128212409480530281249753968920059097893
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step 118: 79858190995082782587346415917970951563389518827950018195886
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step 119: 148717372001055664185682931825942903027768047556009927381783
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step 120: 535901101901711405053403241075471042314349514106110201099624
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step 130: 11038412282201773190197163207155755071236070199226820217222474001
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step 131: 21085834553404635489304226424211510241472249308364530445443957012
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step 138: 13712010365863952926161109273168488957514819110615302503595531202172
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step 140: 71764447740798955565524591240378954888393219553555465889804764447707
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step 141: 142538894481697812021060182479767800875697439096112021879509538894424
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step 142: 567037730387675932232751117276345809643671720156232240675694037729665
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step 143: 1133965460884251974465402144452692718187344431313464480252477075460430
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step 144: 1474611168626772819108533488890510891149888843359109271777357721153741
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step 145: 2948122446164544548128066977779922871300877686717128454553626332318482
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step 147: 10592609554856108192780477691120018218200210966750783818916485649063949
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step 148: 105528704213318090031486244592320299499202330644159512999082331239693450
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step 149: 159925636346599089247437690625523294491225626086843643089895643647518951
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step 152: 1048273630861683270565224505907391747746093709614432554073476258135382740
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step 153: 1521108949388426975117568674981298225218030804668658204797337938499111141
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step 154: 2932228897785764949146137339061606350446952699437315320593586777997122392
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step 155: 5864446895562618899381274689024202790983014308774631740088262655985344784
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step 156: 10738882791125247699852639467058306681955038518639353580076425311971789469
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step 157: 107237600702477714708388033148641362600615423595132979479750677431700673170
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step 158: 178613607837253772683367264743965878606878570436463863287168451638707405871
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step 159: 357118315673408634465735629378041757213757139783926626673445804377413722742
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step 160: 604345630446817178842362258765973514526514280657853164237882608753927534495
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step 161: 1198781359804623467574823617522055930151929660225705427486754327397964077901
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step 162: 2296486057741858044422068692742725221662325162482868712244397591487495956812
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step 163: 4483082005583815978844247375585340454323550434955837314488806172965002803734
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step 164: 8856164011276532067688384761179681007558090870811574738977601356820005607578
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step 165: 17613229011563063135486759512360461916115092740523249577845203713541110224166
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step 166: 83755430126094793390364353744865190967277009146844845346298339750052202455837
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step 167: 157610850351100586779628708589729381044553918303689580692607679499114305911575
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step 168: 732730353763095563485924794576033200399994102231675388519585364500267363928326
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step 169: 1356559717525101027071840678152165401899987104562350885949169730090634716965563
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step 170: 5012255891886001406691336558684819419799968150174869646430876931105891896522094
+ 4902256981985011396780346469684710518699979149184868556331966041006881985522105
step 171: 9914512873871012803471683028369529938499947299359738202762842972112773882044199
+ 9914402883772112792482672028379539927499948399259638203861743082101783782154199
step 172: 19828915757643125595954355056749069865999895698619376406624586054214557664198398
+ 89389146675541245068542660467391689659899956896094765055345959552134675751982891
step 173: 109218062433184370664497015524140759525899852594714141461970545606349233416181289
+ 982181614332943606545079164141417495258998525957041425510794466073481334260812901
step 174: 1091399676766127977209576179665558254784898378551755566972765011679830567676994190
+ 0914996767650389761105672796655571558738984874528555669716759027797216676769931901
step 175: 2006396444416517738315248976321129813523883253080311236689524039477047244446926091
+ 1906296444427407749304259866321130803523883253189211236798425138377156144446936002
step 176: 3912692888843925487619508842642260617047766506269522473487949177854203388893862093
+ 3902683988833024587719497843742259626056677407160622462488059167845293488882962193
step 177: 7815376877676950075339006686384520243104443913430144935976008345699496877776824286
+ 6824286777786949965438006795394410343193444013420254836866009335700596767786735187
step 178: 14639663655463900040777013481778930586297887926850399772842017681400093645563559473
+ 37495536554639000418671024827799305862978879268503987718431077704000936455636693641
step 179: 52135200210102900459448038309578236449276767195354387491273095385401030101200253114
+ 41135200210103010458359037219478345359176767294463287590383084495400920101200253125
step 180: 93270400420205910917807075529056581808453534489817675081656179880801950202400506239
+ 93260500420205910808897165618057671898443535480818565092557070871901950202400407239
step 181: 186530900840411821726704241147114253706897069970636240174213250752703900404800913478
+ 874319008404009307257052312471042636079960798607352411741142407627128114048009035681
step 182: 1060849909244421128983756553618156889786857868577988651915355658379832014452809949159
+ 9519499082544102389738565535191568897758687586879886518163556573898211244429099480601
step 183: 10580348991788523518722322088809725787545545455457875170078912232278043258881909429760
+ 06792490918885234087223221987007157875455454554578752790888022322781532588719984308501
step 184: 17372839910673757605945544075816883663001000010036627960966934555059575847601893738261
+ 16283739810674857595055543966906972663001000010036638861857044554950675737601993827371
step 185: 33656579721348615201001088042723856326002000020073266822823979110010251585203887565632
+ 23656578830258515201001197932822866237002000020062365832724088010010251684312797565633
step 186: 57313158551607130402002285975546722563004000040135632655548067120020503269516685131265
+ 56213158661596230502002176084555623653104000040036522764557958220020403170615585131375
step 187: 113526317213203360904004462060102346216108000080172155420106025340040906440132270262640
+ 046262072231044609040043520601024551271080000801612643201060264400409063302312713625311
step 188: 159788389444247969944047982661126897487188000881784798621166289740449969742444983887951
|
|
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1600402195090 takes 188 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 2,542,468 times since Saturday, March 9th, 2002.)
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