|
REVERSAL-ADDITION
PALINDROME
TEST ON
10000696511
|
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 10000696511: |
10000696511
+ 11569600001
step 1: 21570296512
+ 21569207512
step 2: 43139504024
+ 42040593134
step 3: 85180097158
+ 85179008158
step 4: 170359105316
+ 613501953071
step 5: 783861058387
+ 783850168387
step 6: 1567711226774
+ 4776221177651
step 7: 6343932404425
+ 5244042393436
step 8: 11587974797861
+ 16879747978511
step 9: 28467722776372
+ 27367722776482
step 10: 55835445552854
+ 45825554453855
step 11: 101661000006709
+ 907600000166101
step 12: 1009261000172810
+ 0182710001629001
step 13: 1191971001801811
+ 1181081001791911
step 14: 2373052003593722
+ 2273953002503732
step 15: 4647005006097454
+ 4547906005007464
step 16: 9194911011104918
+ 8194011101194919
step 17: 17388922112299837
+ 73899221122988371
step 18: 91288143235288208
+ 80288253234188219
step 19: 171576396469476427
+ 724674964693675171
step 20: 896251361163151598
+ 895151361163152698
step 21: 1791402722326304296
+ 6924036232272041971
step 22: 8715438954598346267
+ 7626438954598345178
step 23: 16341877909196691445
+ 54419669190977814361
step 24: 70761547100174505806
+ 60850547100174516707
step 25: 131612094200349022513
+ 315220943002490216131
step 26: 446833037202839238644
+ 446832938202730338644
step 27: 893665975405569577288
+ 882775965504579566398
step 28: 1776441940910149143686
+ 6863419410190491446771
step 29: 8639861351100640590457
+ 7540950460011531689368
step 30: 16180811811112172279825
+ 52897227121111811808161
step 31: 69078038932223984087986
+ 68978048932223983087096
step 32: 138056087864447967175082
+ 280571769744468780650831
step 33: 418627857608916747825913
+ 319528747619806758726814
step 34: 738156605228723506552727
+ 727255605327822506651837
step 35: 1465412210556546013204564
+ 4654023106456550122145641
step 36: 6119435317013096135350205
+ 5020535316903107135349116
step 37: 11139970633916203270699321
+ 12399607230261933607993111
step 38: 23539577864178136878692432
+ 23429687863187146877593532
step 39: 46969265727365283756285964
+ 46958265738256372756296964
step 40: 93927531465621656512582928
+ 82928521565612656413572939
step 41: 176856053031234312926155867
+ 768551629213432130350658671
step 42: 945407682244666443276814538
+ 835418672344666442286704549
step 43: 1780826354589332885563519087
+ 7809153655882339854536280871
step 44: 9589980010471672740099799958
+ 8599979900472761740100899859
step 45: 18189959910944434480200699817
+ 71899600208443444901995998181
step 46: 90089560119387879382196697998
+ 89979669128397878391106598009
step 47: 180069229247785757773303296007
+ 700692303377757587742922960081
step 48: 880761532625543345516226256088
+ 880652622615543345526235167088
step 49: 1761414155241086691042461423176
+ 6713241642401966801425514141671
step 50: 8474655797643053492467975564847
+ 7484655797642943503467975564748
step 51: 15959311595285996995935951129595
+ 59592115953959969958259511395951
step 52: 75551427549245966954195462525546
+ 64552526459145966954294572415557
step 53: 140103954008391933908490034941103
+ 301149430094809339193800459301041
step 54: 441253384103201273102290494242144
+ 441242494092201372102301483352144
step 55: 882495878195402645204591977594288
+ 882495779195402546204591878594288
step 56: 1764991657390805191409183856188576
+ 6758816583819041915080937561994671
step 57: 8523808241209847106490121418183247
+ 7423818141210946017489021428083258
step 58: 15947626382420793123979142846266505
+ 50566264824197932139702428362674951
step 59: 66513891206618725263681571208941456
+ 65414980217518636252781660219831566
step 60: 131928871424137361516463231428773022
+ 220377824132364615163731424178829131
step 61: 352306695556501976680194655607602153
+ 351206706556491086679105655596603253
step 62: 703513402112993063359300311204205406
+ 604502402113003953360399211204315307
step 63: 1308015804225997016719699522408520713
+ 3170258042259969176107995224085108031
step 64: 4478273846485966192827694746493628744
+ 4478263946474967282916695846483728744
step 65: 8956537792960933475744390592977357488
+ 8847537792950934475743390692977356598
step 66: 17804075585911867951487781285954714086
+ 68041745958218778415976811958557040871
step 67: 85845821544130646367464593244511754957
+ 75945711544239546476364603144512854858
step 68: 161791533088370192843829196389024609815
+ 518906420983691928348291073880335197161
step 69: 680697954072062121192120270269359806976
+ 679608953962072021291121260270459796086
step 70: 1360306908034134142483241530539819603062
+ 2603069189350351423842414314308096030631
step 71: 3963376097384485566325655844847915633693
+ 3963365197484485565236655844837906733693
step 72: 7926741294868971131562311689685822367386
+ 6837632285869861132651311798684921476297
step 73: 14764373580738832264213623488370743843683
+ 38634834707388432631246223883708537346741
step 74: 53399208288127264895459847372079281190424
+ 42409118297027374895459846272188280299335
step 75: 95808326585154639790919693644267561489759
+ 95798416576244639691909793645158562380859
step 76: 191606743161399279482829487289426123870618
+ 816078321624982784928284972993161347606191
step 77: 1007685064786382064411114460282587471476809
+ 9086741747852820644111144602836874605867001
step 78: 10094426812639202708522259063119462077343810
+ 01834377026491136095222580720293621862449001
step 79: 11928803839130338803744839783413083939792811
+ 11829793938031438793844730883303193830882911
step 80: 23758597777161777597589570666716277770675722
+ 22757607777261766607598579577716177779585732
step 81: 46516205554423544205188150244432455550261454
+ 45416205555423444205188150244532445550261564
step 82: 91932411109846988410376300488964901100523018
+ 81032500110946988400367301488964890111423919
step 83: 172964911220793976810743601977929791211946937
+ 739649112197929779106347018679397022119469271
step 84: 912614023418723755917090620657326813331416208
+ 802614133318623756026090719557327814320416219
step 85: 1715228156737347511943181340214654627651832427
+ 7242381567264564120431813491157437376518225171
step 86: 8957609724001911632374994831372092004170057598
+ 8957500714002902731384994732361191004279067598
step 87: 17915110438004814363759989563733283008449125196
+ 69152194480038233736598995736341840083401151971
step 88: 87067304918043048100358985300075123091850277167
+ 76177205819032157000358985300184034081940376078
step 89: 163244510737075205100717970600259157173790653245
+ 542356097371751952006079717001502570737015442361
step 90: 705600608108827157106797687601761727910806095606
+ 606590608019727167106786797601751728801806006507
step 91: 1312191216128554324213584485203513456712612102113
+ 3112012162176543153025844853124234558216121912131
step 92: 4424203378305097477239429338327748014928734014244
+ 4424104378294108477238339249327747905038733024244
step 93: 8848307756599205954477768587655495919967467038488
+ 8848307647699195945567858677744595029956577038488
step 94: 17696615404298401900045627265400090949924044076976
+ 67967044042994909000456272654000910489240451669671
step 95: 85663659447293310900501899919401001439164495746647
+ 74664759446193410010491999810500901339274495636658
step 96: 160328418893486720910993899729901902778438991383305
+ 503383199834877209109927998399019027684398814823061
step 97: 663711618728363930020921898128920930462837806206366
+ 663602608738264039029821898129020039363827816117366
step 98: 1327314227466627969050743796257940969826665622323732
+ 2373232265666289690497526973470509697266647224137231
step 99: 3700546493132917659548270769728450667093312846460963
+ 3690646482133907660548279670728459567192313946450073
step 100: 7391192975266825320096550440456910234285626792911036
+ 6301192976265824320196540440556900235286625792911937
step 101: 13692385951532649640293090881013810469572252585822973
+ 37922858525227596401831018809039204694623515958329631
step 102: 51615244476760246042124109690053015164195768544152604
+ 40625144586759146151035009690142124064206767444251615
step 103: 92240389063519392193159119380195139228402535988404219
+ 91240488953520482293159108391195139129391536098304229
step 104: 183480878017039874486318227771390278357794072086708448
+ 844807680270497753872093177722813684478930710878084381
step 105: 1028288558287537628358411405494203962836724782964792829
+ 9282974692874276382693024945041148538267357828558828201
step 106: 10311263251161814011051436350535352501104082611523621030
+ 03012632511628040110525353505363415011041816115236211301
step 107: 13323895762789854121576789855898767512145898726759832331
|
|
|
10000696511 takes 107 iterations / steps to resolve into a 56 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 2,542,409 times since Saturday, March 9th, 2002.)
|