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REVERSAL-ADDITION
PALINDROME
TEST ON
1000043902320
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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 1000043902320: |
1000043902320
+ 0232093400001
step 1: 1232137302321
+ 1232037312321
step 2: 2464174614642
+ 2464164714642
step 3: 4928339329284
+ 4829239338294
step 4: 9757578667578
+ 8757668757579
step 5: 18515247425157
+ 75152474251581
step 6: 93667721676738
+ 83767612776639
step 7: 177435334453377
+ 773354433534771
step 8: 950789767988148
+ 841889767987059
step 9: 1792679535975207
+ 7025795359762971
step 10: 8818474895738178
+ 8718375984748188
step 11: 17536850880486366
+ 66368408805863571
step 12: 83905259686349937
+ 73994368695250938
step 13: 157899628381600875
+ 578006183826998751
step 14: 735905812208599626
+ 626995802218509537
step 15: 1362901614427109163
+ 3619017244161092631
step 16: 4981918858588201794
+ 4971028858588191894
step 17: 9952947717176393688
+ 8863936717177492599
step 18: 18816884434353886287
+ 78268835343448861881
step 19: 97085719777802748168
+ 86184720877791758079
step 20: 183270440655594506247
+ 742605495556044072381
step 21: 925875936211638578628
+ 826875836112639578529
step 22: 1752751772324278157157
+ 7517518724232771572571
step 23: 9270270496557049729728
+ 8279279407556940720729
step 24: 17549549904113990450457
+ 75405409931140994594571
step 25: 92954959835254985045028
+ 82054058945253895945929
step 26: 175009018780508880990957
+ 759099088805087810900571
step 27: 934108107585596691891528
+ 825198196695585701801439
step 28: 1759306304281182393692967
+ 7692963932811824036039571
step 29: 9452270237093006429732538
+ 8352379246003907320722549
step 30: 17804649483096913750455087
+ 78055405731969038494640871
step 31: 95860055215065952245095958
+ 85959054225956051255006859
step 32: 181819109441022003500102817
+ 718201005300220144901918181
step 33: 900020114741242148402020998
+ 899020204841242147411020009
step 34: 1799040319582484295813041007
+ 7001403185924842859130409971
step 35: 8800443505507327154943450978
+ 8790543494517237055053440088
step 36: 17590987000024564209996891066
+ 66019869990246542000078909571
step 37: 83610856990271106210075800637
+ 73600857001260117209965801638
step 38: 157211713991531223420041602275
+ 572206140024322135199317112751
step 39: 729417854015853358619358715026
+ 620517853916853358510458714927
step 40: 1349935707932706717129817429953
+ 3599247189217176072397075399431
step 41: 4949182897149882789526892829384
+ 4839282986259872889417982819494
step 42: 9788465883409755678944875648878
+ 8788465784498765579043885648879
step 43: 18576931667908521257988761297757
+ 75779216788975212580976613967581
step 44: 94356148456883733838965375265338
+ 83356257356983833738865484165349
step 45: 177712405813867567577830859430687
+ 786034958038775765768318504217771
step 46: 963747363852643333346149363648458
+ 854846363941643333346258363747369
step 47: 1818593727794286666692407727395827
+ 7285937277042966666824977273958181
step 48: 9104531004837253333517385001354008
+ 8004531005837153333527384001354019
step 49: 17109062010674406667044769002708027
+ 72080720096744076660447601026090171
step 50: 89189782107418483327492370028798198
+ 89189782007329472338481470128798198
step 51: 178379564114747955665973840157596396
+ 693695751048379566559747411465973871
step 52: 872075315163127522225721251623570267
+ 762075326152127522225721361513570278
step 53: 1634150641315255044451442613137140545
+ 5450417313162441544405525131460514361
step 54: 7084567954477696588856967744597654906
+ 6094567954477696588856967744597654807
step 55: 13179135908955393177713935489195309713
+ 31790359198453931777139355980953197131
step 56: 44969495107409324954853291470148506844
+ 44860584107419235845942390470159496944
step 57: 89830079214828560800795681940308003788
+ 88730080304918659700806582841297003898
step 58: 178560159519747220501602264781605007686
+ 686700506187462206105022747915951065871
step 59: 865260665707209426606625012697556073557
+ 755370655796210526606624902707566062568
step 60: 1620631321503419953213249915405122136125
+ 5216312215045199423123599143051231360261
step 61: 6836943536548619376336849058456353496386
+ 6836943536548509486336739168456353496386
step 62: 13673887073097128862673588226912706992772
+ 27729960721962288537626882179037078837631
step 63: 41403847795059417400300470405949785830403
+ 30403858794950407400300471495059774830414
step 64: 71807706590009824800600941901009560660817
+ 71806606590010914900600842890009560770817
step 65: 143614313180020739701201784791019121431634
+ 436134121910197487102107937020081313416341
step 66: 579748435090218226803309721811100434847975
+ 579748434001118127903308622812090534847975
step 67: 1159496869091336354706618344623190969695950
+ 0595969690913264438166074536331909686949511
step 68: 1755466560004600792872692880955100656645461
+ 1645466560015590882962782970064000656645571
step 69: 3400933120020191675835475851019101313291032
+ 2301923131019101585745385761910200213390043
step 70: 5702856251039293261580861612929301526681075
+ 5701866251039292161680851623929301526582075
step 71: 11404722502078585423261713236858603053263150
+ 05136235030685863231716232458587020522740411
step 72: 16540957532764448654977945695445623576003561
+ 16530067532654459654977945684446723575904561
step 73: 33071025065418908309955891379892347151908122
+ 22180915174329897319855990380981456052017033
step 74: 55251940239748805629811881760873803203925155
+ 55152930230837806718811892650884793204915255
step 75: 110404870470586612348623774411758596408840410
+ 014048804695857114477326843216685074078404011
step 76: 124453675166443726825950617628443670487244421
+ 124442784076344826716059528627344661576354421
step 77: 248896459242788553542010146255788332063598842
+ 248895360233887552641010245355887242954698842
step 78: 497791819476676106183020391611675575018297684
+ 486792810575576116193020381601676674918197794
step 79: 984584630052252222376040773213352249936495478
+ 874594639942253312377040673222252250036485489
step 80: 1859179269994505534753081446435604499972980967
+ 7690892799944065346441803574355054999629719581
step 81: 9550072069938570881194885020790659499602700548
+ 8450072069949560970205884911880758399602700559
step 82: 18000144139888131851400769932671417899205401107
+ 70110450299871417623996700415813188893144100081
step 83: 88110594439759549475397470348484606792349501188
+ 88110594329760648484307479357494595793449501188
step 84: 176221188769520197959704949705979202585799002376
+ 673200997585202979507949407959791025967881122671
step 85: 849422186354723177467654357665770228553680125047
+ 740521086355822077566753456764771327453681224948
step 86: 1589943272710545255034407814430541556007361349995
+ 5999431637006551450344187044305525450172723499851
step 87: 7589374909717096705378594858736067006180084849846
+ 6489484800816007606378584958735076907179094739857
step 88: 14078859710533104311757179817471143913359179589703
+ 30798597195331934117471897175711340133501795887041
step 89: 44877456905865038429229076993182484046860975476744
+ 44767457906864048428139967092292483056850965477844
step 90: 89644914812729086857369044085474967103711940954588
+ 88545904911730176947458044096375868092721841944698
step 91: 178190819724459263804827088181850835196433782899286
+ 682998287334691538058181880728408362954427918091871
step 92: 861189107059150801863008968910259198150861700991157
+ 751199007168051891952019869800368108051950701981168
step 93: 1612388114227202693815028838710627306202812402972325
+ 5232792042182026037260178388205183962027224118832161
step 94: 6845180156409228731075207226915811268230036521804486
+ 6844081256300328621185196227025701378229046510815486
step 95: 13689261412709557352260403453941512646459083032619972
+ 27991623038095464621514935430406225375590721416298631
step 96: 41680884450805021973775338884347738022049804448918603
+ 30681984440894022083774348883357737912050805448808614
step 97: 72362868891699044057549687767705475934100609897727217
+ 71272779890600143957450776778694575044099619886826327
step 98: 143635648782299188015000464546400050978200229784553544
+ 445355487922002879050004645464000510881992287846536341
step 99: 588991136704302067065005110010400561860192517631089885
+ 588980136715291068165004010011500560760203407631199885
step 100: 1177971273419593135230009120021901122620395925262289770
+ 0779822625295930262211091200219000325313959143721797711
step 101: 1957793898715523397441100320240901447934355068984087481
+ 1847804898605534397441090420230011447933255178983977591
step 102: 3805598797321057794882190740470912895867610247968065072
+ 2705608697420167685982190740470912884977501237978955083
step 103: 6511207494741225480864381480941825780845111485947020155
+ 5510207495841115480875281490841834680845221474947021156
step 104: 12021414990582340961739662971783660461690332960894041311
+ 11314049806923309616406638717926693716904328509941412021
step 105: 23335464797505650578146301689710354178594661470835453332
+ 23335453807416649587145301798610364187505650579746453332
step 106: 46670918604922300165291603488320718366100312050581906664
+ 46660918505021300166381702388430619256100322940681907664
step 107: 93331837109943600331673305876751337622200634991263814328
+ 82341836219943600222673315767850337613300634990173813339
step 108: 175673673329887200554346621644601675235501269981437627667
+ 766726734189962105532576106446126643455002788923376376571
step 109: 942400407519849306086922728090728318690504058904814004238
+ 832400418409850405096813827090827229680603948915704004249
step 110: 1774800825929699711183736555181555548371108007820518008487
+ 7848008150287008011738455551815556373811179969295280084771
step 111: 9622808976216707722922192106997111922182287977115798093258
+ 8523908975117797822812291117996012912292277076126798082269
step 112: 18146717951334505545734483224993124834474565053242596175527
+ 72557169524235056547443842139942238443754550543315971764181
step 113: 90703887475569562093178325364935363278229115596558567939708
+ 80793976585569551192287236353946352387139026596557478830709
step 114: 171497864061139113285465561718881715665368142193116046770417
+ 714077640611391241863566517188817165564582311931160468794171
step 115: 885575504672530355149032078907698881229950454124276515564588
+ 885465515672421454059922188896709870230941553035276405575588
step 116: 1771041020344951809208954267804408751460892007159552921140176
+ 6710411292559517002980641578044087624598029081594430201401771
step 117: 8481452312904468812189595845848496376058921088753983122541947
+ 7491452213893578801298506736948485485959812188644092132541848
step 118: 15972904526798047613488102582796981862018733277398075255083795
+ 59738055257089377233781026818969728520188431674089762540927951
step 119: 75710959783887424847269129401766710382207164951487837796011746
+ 64711069773878415946170228301766710492196274842478838795901757
step 120: 140422029557765840793439357703533420874403439793966676591913503
+ 305319195676669397934304478024335307753934397048567755920224041
step 121: 445741225234435238727743835727868728628337836842534432512137544
+ 445731215234435248638733826827868727538347727832534432522147544
step 122: 891472440468870487366477662555737456166685564675068865034285088
+ 880582430568860576465586661654737555266774663784078864044274198
step 123: 1772054871037731063832064324210475011433460228459147729078559286
+ 6829558709277419548220643341105740124234602383601377301784502771
step 124: 8601613580315150612052707665316215135668062612060525030863062057
+ 7502603680305250602162608665315126135667072502160515130853161068
step 125: 16104217260620401214215316330631341271335135114221040161716223125
+ 52132261716104012241153153317214313603361351241210402606271240161
step 126: 68236478976724413455368469647845654874696486355431442767987463286
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1000043902320 takes 126 iterations / steps to resolve into a 65 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
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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 2,549,992 times since Saturday, March 9th, 2002.)
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