REVERSAL-ADDITION
PALINDROME
TEST ON
10000973037
|
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 10000973037: |
10000973037
+ 73037900001
step 1: 83038873038
+ 83037883038
step 2: 166076756076
+ 670657670661
step 3: 836734426737
+ 737624437638
step 4: 1574358864375
+ 5734688534751
step 5: 7309047399126
+ 6219937409037
step 6: 13528984808163
+ 36180848982531
step 7: 49709833790694
+ 49609733890794
step 8: 99319567681488
+ 88418676591399
step 9: 187738244272887
+ 788272442837781
step 10: 976010687110668
+ 866011786010679
step 11: 1842022473121347
+ 7431213742202481
step 12: 9273236215323828
+ 8283235126323729
step 13: 17556471341647557
+ 75574614317465571
step 14: 93131085659113128
+ 82131195658013139
step 15: 175262281317126267
+ 762621713182262571
step 16: 937883994499388838
+ 838883994499388739
step 17: 1776767988998777577
+ 7757778998897676771
step 18: 9534546987896454348
+ 8434546987896454359
step 19: 17969093975792908707
+ 70780929757939096971
step 20: 88750023733732005678
+ 87650023733732005788
step 21: 176400047467464011466
+ 664110464764740004671
step 22: 840510512232204016137
+ 731610402232215015048
step 23: 1572120914464419031185
+ 5811309144644190212751
step 24: 7383430059108609243936
+ 6393429068019500343837
step 25: 13776859127128109587773
+ 37778590182172195867731
step 26: 51555449309300305455504
+ 40555450300390394455515
step 27: 92110899609690699911019
+ 91011999609690699801129
step 28: 183122899219381399712148
+ 841217993183912998221381
step 29: 1024340892403294397933529
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step 30: 10277738827326337378367730
+ 03776387373362372883777201
step 31: 14054126200688710262144931
+ 13944126201788600262145041
step 32: 27998252402477310524289972
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step 33: 55996494903854730949579944
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step 34: 100994089807600561899049899
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step 35: 1099935087972607270879548900
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step 37: 2286889737300440037369887712
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step 38: 4464779374600880074749774534
+ 4354779474700880064739774644
step 39: 8819558849301760139489549178
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step 40: 17539018698612431178978108366
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step 41: 83919206685725852868659201937
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step 42: 157829502372551705627319493875
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+ 626224525009068850990614422637
step 44: 1362448941108127711891139845263
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step 45: 4987938253089304929902638287894
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step 46: 9975766615188598969706166685788
+ 8875866616079698958815166675799
step 47: 18851633231268297928521333361587
+ 78516333312582979286213233615881
step 48: 97367966543851277214734566977468
+ 86477966543741277215834566976379
step 49: 183845933087592554430569133953847
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step 50: 932205265052627009726349473502228
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step 51: 1754410639996254910452600036004467
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step 52: 9398416940058795104979599396149038
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step 53: 17707833880018589120958099892297977
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step 54: 95687063779104491319539108726168748
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step 55: 180473226559298082638979306462247407
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step 56: 885215491163277918919872262084621488
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step 57: 1769341971425556838739644623279134076
+ 6704319723264469378386555241791439671
step 58: 8473661694690026217126199865070573747
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step 59: 15947412400379942434252400830032237495
+ 59473223003800425243424997300421474951
step 60: 75420635404180367677677398130453712446
+ 64421735403189377677676308140453602457
step 61: 139842370807369745355353706270907314903
+ 309413709072607353553547963708073248931
step 62: 449256079879977098908901669978980563834
+ 438365089879966109809890779978970652944
step 63: 887621169759943208718792449957951216778
+ 877612159759944297817802349957961126788
step 64: 1765233329519887506536594799915912343566
+ 6653432195199974956356057889159233325671
step 65: 8418665524719862462892652689075145669237
+ 7329665415709862562982642689174255668148
step 66: 15748330940429725025875295378249401337385
+ 58373310494287359257852052792404903384751
step 67: 74121641434717084283727348170654304722136
+ 63122740345607184372738248071743414612147
step 68: 137244381780324268656465596242397719334283
+ 382433917793242695564656862423087183442731
step 69: 519678299573566964221122458665484902777014
+ 410777209484566854221122469665375992876915
step 70: 930455509058133818442244928330860895653929
+ 929356598068033829442244818331850905554039
step 71: 1859812107126167647884489746662711801207968
+ 8697021081172666479844887467616217012189581
step 72: 10556833188298834127729377214278928813397549
+ 94579331882987241277392772143889288133865501
step 73: 105136165071286075405122149358168216947263050
+ 050362749612861853941221504570682170561631501
step 74: 155498914684147929346343653928850387508894551
+ 155498805783058829356343643929741486419894551
step 75: 310997720467206758702687297858591873928789102
+ 201987829378195858792786207857602764027799013
step 76: 512985549845402617495473505716194637956588115
+ 511885659736491617505374594716204548945589215
step 77: 1024871209581894235000848100432399186902177330
+ 0337712096819932340018480005324981859021784201
step 78: 1362583306401826575019328105757381045923961531
+ 1351693295401837575018239105756281046033852631
step 79: 2714276601803664150037567211513662091957814162
+ 2614187591902663151127657300514663081066724172
step 80: 5328464193706327301165224512028325173024538334
+ 4338354203715238202154225611037236073914648235
step 81: 9666818397421565503319450123065561246939186569
+ 9656819396421655603210549133055651247938186669
step 82: 19323637793843221106529999256121212494877373238
+ 83237377849421212165299992560112234839773632391
step 83: 102561015643264433271829991816233447334651005629
+ 926500156433744332618199928172334462346510165201
step 84: 1029061172077008765890029919988567909681161170830
+ 0380711611869097658899199200985678007702711609201
step 85: 1409772783946106424789229120974245917383872780031
+ 1300872783837195424790219229874246016493872779041
step 86: 2710645567783301849579448350848491933877745559072
+ 2709555477783391948480538449759481033877655460172
step 87: 5420201045566693798059986800607972967755401019244
+ 4429101045577692797060086899508973966655401020245
step 88: 9849302091144386595120073700116946934410802039489
+ 9849302080144396496110073700215956834411902039489
step 89: 19698604171288783091230147400332903768822704078978
+ 87987040722886730923300474103219038788217140689691
step 90: 107685644894175514014530621503551942557039844768669
+ 966867448930755249155305126035410415571498446586701
step 91: 1074553093824930763169835747538962358128538291355370
+ 0735531928358218532698357475389613670394283903554701
step 92: 1810085022183149295868193222928576028522822194910071
+ 1700194912282258206758292223918685929413812205800181
step 93: 3510279934465407502626485446847261957936634400710252
+ 2520170044366397591627486445846262057045644399720153
step 94: 6030449978831805094253971892693524014982278800430405
+ 5040340088722894104253962981793524905081388799440306
step 95: 11070790067554699198507934874487048920063667599870711
+ 11707899576636002984078447843970589199645576009707011
step 96: 22778689644190702182586382718457638119709243609577722
+ 22777590634290791183675481728368528120709144698687722
step 97: 45556280278481493366261864446826166240418388308265444
+ 44456280388381404266162864446816266339418487208265554
step 98: 90012560666862897632424728893642432579836875516530998
+ 89903561557863897523424639882742423679826866606521009
step 99: 179916122224726795155849368776384856259663742123052007
+ 700250321247366952658483677863948551597627422221619971
step 100: 880166443472093747814333046640333407857291164344671978
+ 879176443461192758704333046640333418747390274344661088
step 101: 1759342886933286506518666093280666826604681438689333066
+ 6603339868341864066286660823906668156056823396882439571
step 102: 8362682755275150572805326917187334982661504835571772637
+ 7362771755384051662894337817196235082750515725572862638
step 103: 15725454510659202235699664734383570065412020561144635275
+ 57253644116502021456007538343746699653220295601545452751
step 104: 72979098627161223691707203078130269718632316162690088026
+ 62088009626161323681796203187030270719632216172689097927
step 105: 135067108253322547373503406265160540438264532335379185953
+ 359581973533235462834045061562604305373745223352801760531
step 106: 494649081786558010207548467827764845812009755688180946484
+ 484649081886557900218548467728764845702010855687180946494
step 107: 979298163673115910426096935556529691514020611375361892978
+ 879298163573116020415196925655539690624019511376361892979
step 108: 1858596327246231930841293861212069382138040122751723785957
+ 7595873271572210408312839602121683921480391326427236958581
step 109: 9454469598818442339154133463333753303618431449178960744538
+ 8354470698719441348163033573333643314519332448188959644549
step 110: 17808940297537883687317167036667396618137763897367920389087
+ 78098302976379836773181669376663076171378638873579204980871
step 111: 95907243273917720460498836413330472789516402770947125369958
+ 85996352174907720461598727403331463889406402771937234270959
step 112: 181903595448825440922097563816661936678922805542884359640917
+ 719046953488245508229876639166618365790229044528844595309181
step 113: 900950548937070949151974202983280302469151850071728954950098
+ 890059459827170058151964203082389202479151949070739845059009
step 114: 1791010008764241007303938406065669504948303799142468800009107
+ 7019000088642419973038494059665606048393037001424678000101971
step 115: 8810010097406660980342432465731275553341340800567146800111078
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step 116: 17511120183824311060773866021452651195683771691233194700211266
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step 117: 83722320932957530678512525137078063262521477702576032802322837
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step 118: 157544641756025051455925051373165136415043065306151956704645575
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step 119: 733091049415176655016265566004726509565572619456672613851091326
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step 120: 1356281207731453309932541131910353910231135230013344128791281663
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step 121: 5018103185945886410257852452103884101542587629046885505813108194
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step 122: 9936116371001772819525704903118767114085175149193771001626126299
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step 123: 19862332632003546738941420707236445227179250408376542003362242698
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step 124: 109486558962028114119346717879490908497881665392141072026985569589
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step 125: 1095452148582298255412912906674300003476599309303552892296841254490
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step 126: 2039973635505280808451952863417300038242691501449081815155253800391
+ 1930083525515181809441051962428300037143682591548080825055363799302
step 127: 3970057161020462617893004825845600075386374092997162640210617599693
+ 3969957160120462617992904736835700065485284003987162640201617500793
step 128: 7940014321140925235885909562681300140871658096984325280412235100486
+ 6840015322140825234896908561780410031862659095885325290411234100497
step 129: 14780029643281750470782818124461710172734317192869650570823469200983
+ 38900296432807505696829171343727101716442181828707405718234692008741
step 130: 53680326076089256167611989468188811889176499021577056289058161209724
+ 42790216185098265077512099467198811888186498911676165298067062308635
step 131: 96470542261187521245124088935387623777362997933253221587125223518359
+ 95381532252178512235233979926377732678353988042154212578116224507469
step 132: 191852074513366033480358068861765356455716985975407434165241448025828
+ 828520844142561434704579589617554653567168860853084330663315470258191
step 133: 1020372918655927468184937658479320010022885846828491764828556918284019
+ 9104828196558284671948286485882200100239748567394818647295568192730201
step 134: 10125201115214212140133224144361520110262634414223310412124125111014220
+ 02241011152142121401332241443626201102516344142233104121241251110252101
step 135: 12366212267356333541465465587987721212778978556456414533365376221266321
|
|
10000973037 takes 135 iterations / steps to resolve into a 71 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.)
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!
|
[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 2,531,709 times since Saturday, March 9th, 2002.)
|