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REVERSAL-ADDITION
PALINDROME
TEST ON
100079239995161
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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 100079239995161: |
100079239995161
+ 161599932970001
step 1: 261679172965162
+ 261569271976162
step 2: 523248444941324
+ 423149444842325
step 3: 946397889783649
+ 946387988793649
step 4: 1892785878577298
+ 8927758785872981
step 5: 10820544664450279
+ 97205446644502801
step 6: 108025991308953080
+ 080359803199520801
step 7: 188385794508473881
+ 188374805497583881
step 8: 376760600006057762
+ 267750600006067673
step 9: 644511200012125435
+ 534521210002115446
step 10: 1179032410014240881
+ 1880424100142309711
step 11: 3059456510156550592
+ 2950556510156549503
step 12: 6010013020313100095
+ 5900013130203100106
step 13: 11910026150516200201
+ 10200261505162001911
step 14: 22110287655678202112
+ 21120287655678201122
step 15: 43230575311356403234
+ 43230465311357503234
step 16: 86461040622713906468
+ 86460931722604016468
step 17: 172921972345317922936
+ 639229713543279129271
step 18: 812151685888597052207
+ 702250795888586151218
step 19: 1514402481777183203425
+ 5243023817771842044151
step 20: 6757426299549025247576
+ 6757425209459926247576
step 21: 13514851509008951495152
+ 25159415980090515841531
step 22: 38674267489099467336683
+ 38663376499098476247683
step 23: 77337643988197943584366
+ 66348534979188934673377
step 24: 143686178967386878257743
+ 347752878683769871686341
step 25: 491439057651156749944084
+ 480449947651156750934194
step 26: 971889005302313500878278
+ 872878005313203500988179
step 27: 1844767010615517001866457
+ 7546681007155160107674481
step 28: 9391448017770677109540938
+ 8390459017760777108441939
step 29: 17781907035531454217982877
+ 77828971245413553070918771
step 30: 95610878280945007288901648
+ 84610988270054908287801659
step 31: 180221866550999915576703307
+ 703307675519999055668122081
step 32: 883529542070998971244825388
+ 883528442179899070245925388
step 33: 1767057984250898041490750776
+ 6770570941408980524897507671
step 34: 8537628925659878566388258447
+ 7448528836658789565298267358
step 35: 15986157762318668131686525805
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step 36: 66838726375505349458461694756
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step 37: 132588342860999700015824478622
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step 38: 359462771371007699084068363853
+ 358363860480996700173177264953
step 39: 717826631852004399257245628806
+ 608826542752993400258136628717
step 40: 1326653174604997799515382257523
+ 3257522835159977994064713566231
step 41: 4584176009764975793580095823754
+ 4573285900853975794679006714854
step 42: 9157461910618951588259102538608
+ 8068352019528851598160191647519
step 43: 17225813930147803186419294186127
+ 72168149291468130874103931852271
step 44: 89393963221615934060523226038398
+ 89383062232506043951612236939398
step 45: 178777025454121978012135462977796
+ 697779264531210879121454520777871
step 46: 876556289985332857133589983755667
+ 766557389985331758233589982655678
step 47: 1643113679970664615367179966411345
+ 5431146699717635164660799763113461
step 48: 7074260379688299780027979729524806
+ 6084259279797200879928869730624707
step 49: 13158519659485500659956849460149513
+ 31594106494865995600558495691585131
step 50: 44752626154351496260515345151734644
+ 44643715154351506269415345162625744
step 51: 89396341308703002529930690314360388
+ 88306341309603992520030780314369398
step 52: 177702682618306995049961470628729786
+ 687927826074169940599603816286207771
step 53: 865630508692476935649565286914937557
+ 755739419682565946539674296805036568
step 54: 1621369928375042882189239583719974125
+ 5214799173859329812882405738299631261
step 55: 6836169102234372695071645322019605386
+ 6835069102235461705962734322019616386
step 56: 13671238204469834401034379644039221772
+ 27712293044697343010443896440283217631
step 57: 41383531249167177411478276084322439403
+ 30493422348067287411477176194213538314
step 58: 71876953597234464822955452278535977717
+ 71777953587225455922846443279535967817
step 59: 143654907184459920745801895558071945534
+ 435549170855598108547029954481709456341
step 60: 579204078040058029292831850039781401875
+ 578104187930058138292920850040870402975
step 61: 1157308265970116167585752700080651804850
+ 0584081560800072575857616110795628037511
step 62: 1741389826770188743443368810876279842361
+ 1632489726780188633443478810776289831471
step 63: 3373879553550377376886847621652569673832
+ 2383769652561267486886737730553559783733
step 64: 5757649206111644863773585352206129457565
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step 65: 11415198422134180717547269813322158925140
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step 66: 15568183544466076992118977956444648076551
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step 67: 31135268188932054973248945022889186263102
+ 20136268198822054984237945023988186253113
step 68: 51271536387754109957486890046877372516215
+ 51261527377864009868475990145778363517215
step 69: 102533063765618119825962880192655736033430
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step 70: 136863701321909208095491792009223096368631
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step 71: 273727391644809505290082594918346203737262
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step 72: 536464694288629000570175100826792397464634
+ 436464793297628001571075000926882496464635
step 73: 972929487586257002141250101753674893929269
+ 962929398476357101052141200752685784929279
step 74: 1935858886062614103193391302506360678858548
+ 8458588760636052031933913014162606888585391
step 75: 10394447646698666135127304316668967567443939
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step 76: 104328924223685327475499457483358632241893240
+ 042398142236853384754994574723586322429823401
step 77: 146727066460538712230494032206944954671716641
+ 146617176459449602230494032217835064660727641
step 78: 293344242919988314460988064424780019332444282
+ 282444233910087424460889064413889919242443392
step 79: 575788476830075738921877128838669938574887674
+ 476788475839966838821778129837570038674887575
step 80: 1052576952670042577743655258676239977249775249
+ 9425779427799326768525563477752400762596752501
step 81: 10478356380469369346269218736428640739846527750
+ 05772564893704682463781296264396396408365387401
step 82: 16250921274174051810050515000825037148211915151
+ 15151911284173052800051505001815047147212905261
step 83: 31402832558347104610102020002640084295424820412
+ 21402842459248004620002020101640174385523820413
step 84: 52805675017595109230104040104280258680948640825
+ 52804684908685208240104040103290159571057650825
step 85: 105610359926280317470208080207570418252006291650
+ 056192600252814075702080802074713082629953016501
step 86: 161802960179094393172288882282283500881959308151
+ 151803959188005382282288882271393490971069208161
step 87: 313606919367099775454577764553676991853028516312
+ 213615820358199676355467775454577990763919606313
step 88: 527222739725299451810045540008254982616948122625
+ 526221849616289452800045540018154992527937222725
step 89: 1053444589341588904610091080026409975144885345350
+ 0535435884415799046200801900164098851439854443501
step 90: 1588880473757387950810892980190508826584739788851
+ 1588879374856288050910892980180597837573740888851
step 91: 3177759848613676001721785960371106664158480677702
+ 2077760848514666011730695871271006763168489577713
step 92: 5255520697128342013452481831642113427326970255415
+ 5145520796237243112461381842543102438217960255525
step 93: 10401041493365585125913863674185215865544930510940
+ 04901503944556851258147636831952158556339414010401
step 94: 15302545437922436384061500506137374421884344521341
+ 14312544348812447373160500516048363422973454520351
step 95: 29615089786734883757222001022185737844857799041692
+ 29614099775844873758122010022275738843768798051692
step 96: 59229189562579757515344011044461476688626597093384
+ 48339079562688667416444011044351575797526598192295
step 97: 107568269125268424931788022088813052486153195285679
+ 976582591351684250318880220887139424862521962865701
step 98: 1084150860476952675250668242975952477348675158151380
+ 0831518515768437742595792428660525762596740680514801
step 99: 1915669376245390417846460671636478239945415838666181
+ 1816668385145499328746361760646487140935426739665191
step 100: 3732337761390889746592822432282965380880842578331372
+ 2731338752480880835692822342282956479880931677332373
step 101: 6463676513871770582285644774565921860761774255663745
+ 5473665524771670681295654774465822850771783156763646
step 102: 11937342038643441263581299549031744711533557412427391
+ 19372421475533511744713094599218536214434683024373911
step 103: 31309763514176953008294394148250280925968240436801302
+ 20310863404286952908205284149349280035967141536790313
step 104: 51620626918463905916499678297599560961935381973591615
+ 51619537918353916906599579287699461950936481962602615
step 105: 103240164836817822823099257585299022912871863936194230
+ 032491639368178219220992585752990328228718638461042301
step 106: 135731804204996042044091843338289351141590502397236531
+ 135632793205095141153982833348190440240699402408137531
step 107: 271364597410091183198074676686479791382289904805374062
+ 260473508409982283197974686676470891381190014795463172
step 108: 531838105820073466396049363362950682763479919600837234
+ 432738006919974367286059263363940693664370028501838135
step 109: 964576112740047833682108626726891376427849948102675369
+ 963576201849948724673198627626801286338740047211675469
step 110: 1928152314589996558355307254353692662766589995314350838
+ 8380534135999856672662963534527035538556999854132518291
step 111: 10308686450589853231018270788880728201323589849446869129
+ 92196864494898532310282708888707281013235898505468680301
step 112: 102505550945488385541300979677588009214559488354915549430
+ 034945519453884955412900885776979003145583884549055505201
step 113: 137451070399373340954201865454567012360143372903971054631
+ 136450179309273341063210765454568102459043373993070154731
step 114: 273901249708646682017412630909135114819186746897041209362
+ 263902140798647681918411531909036214710286646807942109372
step 115: 537803390507294363935824162818171329529473393704983318734
+ 437813389407393374925923171818261428539363492705093308735
step 116: 975616779914687738861747334636432758068836886410076627469
+ 964726670014688638860857234636433747168837786419977616579
step 117: 1940343449929376377722604569272866505237674672830054244048
+ 8404424500382764767325056682729654062277736739299443430491
step 118: 10344767950312141145047661252002520567515411412129497674539
+ 93547679492121411451576502520025216674054114121305976744301
step 119: 103892447442433552596624163772027737241569525533435474418840
+ 048814474534335525965142737720277361426695255334244744298301
step 120: 152706921976769078561766901492305098668264780867680218717141
+ 141717812086768087462866890503294109667165870967679129607251
step 121: 294424734063537166024633791995599208335430651835359348324392
+ 293423843953538156034533802995599197336420661735360437424492
step 122: 587848578017075322059167594991198405671851313570719785748884
+ 488847587917075313158176504891199495761950223570710875848785
step 123: 1076696165934150635217344099882397901433801537141430661597669
+ 9667951660341417351083341097932889904437125360514395616966701
step 124: 10744647826275567986300685197815287805870926897655826278564370
+ 07346587262855679862907850878251879158600368976557262874644701
step 125: 18091235089131247849208536076067166964471295874213089153209071
+ 17090235198031247859217446966176067063580294874213198053219081
step 126: 35181470287162495708425983042243234028051590748426287206428152
+ 25182460278262484709515082043234224038952480759426178207418153
step 127: 60363930565424980417941065085477458067004071507852465413846305
+ 50364831456425870517040076085477458056014971408942456503936306
step 128: 110728762021850850934981141170954916123019042916794921917782611
+ 116287719129497619240910321619459071141189439058058120267827011
step 129: 227016481151348470175891462790413987264208481974853042185609622
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step 130: 453923062391706949360693925579728084528407053049696193370220344
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step 131: 896945135783403889711398751060556060057803116999303386630549698
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step 132: 1793890172466707889322707501121211120215696234987607774162099396
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step 133: 8733792787243775783649672621332332331272768474874684416873083367
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step 134: 16367596573388640568398345342664664662535537938750457844746056745
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step 135: 71132661318264046352371898869311311286889927325255146182315633106
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step 136: 131266312646428201604744897737522622683779744650619192463632256223
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step 137: 453918549010720117661192875123748848421578192056722017109845918354
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step 138: 907738097912430345311484750248597695743156483223433044120791737708
+ 807737197021440334322384651347596795842057484113543034219790837709
step 139: 1715475294933870679633869401596194491585213967336976078340582575417
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step 140: 8861228145372577475971562527448139408536263650706736861735508320588
+ 8850238055371686376070563626358049318447252651795747752735418221688
step 141: 17711466200744263852042126153806188726983516302502484614470926542276
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step 142: 84936029108185912272562487692768976887818678426528320859171192954047
+ 74045929117195802382562487681878867986729678426527221958180192063948
step 143: 158981958225381714655124975374647844874548356853055542817351385017995
+ 599710583153718245550358653845478448746473579421556417183522859189851
step 144: 758692541379099960205483629220126293621021936274611960000874244207846
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step 145: 1407394983857100029321956268340252686242044862659114029991847389504703
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step 146: 4481454821339099233441518952742679548762483489250353230009431284441744
+ 4471444821349000323530529843842678459762472598151443329909331284541844
step 147: 8952899642688099556972048796585358008524956087401796559918762568983588
+ 8853898652678199556971047806594258008535856978402796559908862469982598
step 148: 17806798295366299113943096603179616017060813065804593119827625038966186
+ 68166983052672891139540856031806071061697130669034931199266359289760871
step 149: 85973781348039190253483952634985687078757943734839524319093984328727057
+ 75072782348939091342593843734975787078658943625938435209193084318737958
step 150: 161046563696978281596077796369961474157416887360777959528287068647465015
+ 510564746860782825959777063788614751474169963697770695182879696365640161
step 151: 671611310557761107555854860158576225631586851058548654711166765013105176
+ 671501310567661117456845850158685136522675851068458555701167755013116176
step 152: 1343112621125422225012700710317261362154262702127007210412334520026221352
+ 2531226200254332140127007212072624512631627130170072105222245211262113431
step 153: 3874338821379754365139707922389885874785889832297079315634579731288334783
|
|
|
100079239995161 takes 153 iterations / steps to resolve into a 73 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!
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| [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 2,550,024 times since Saturday, March 9th, 2002.)
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