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REVERSAL-ADDITION
PALINDROME
TEST ON
7007009909
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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 7007009909: |
7007009909
+ 9099007007
step 1: 16106016916
+ 61961060161
step 2: 78067077077
+ 77077076087
step 3: 155144153164
+ 461351441551
step 4: 616495594715
+ 517495594616
step 5: 1133991189331
+ 1339811993311
step 6: 2473803182642
+ 2462813083742
step 7: 4936616266384
+ 4836626166394
step 8: 9773242432778
+ 8772342423779
step 9: 18545584856557
+ 75565848554581
step 10: 94111433411138
+ 83111433411149
step 11: 177222866822287
+ 782228668222771
step 12: 959451535045058
+ 850540535154959
step 13: 1809992070200017
+ 7100020702999081
step 14: 8910012773199098
+ 8909913772100198
step 15: 17819926545299296
+ 69299254562991871
step 16: 87119181108291167
+ 76119280118191178
step 17: 163238461226482345
+ 543284622164832361
step 18: 706523083391314706
+ 607413193380325607
step 19: 1313936276771640313
+ 3130461776726393131
step 20: 4444398053498033444
+ 4443308943508934444
step 21: 8887706997006967888
+ 8887696007996077888
step 22: 17775403005003045776
+ 67754030050030457771
step 23: 85529433055033503547
+ 74530533055033492558
step 24: 160059966110066996105
+ 501699660011669950061
step 25: 661759626121736946166
+ 661649637121626957166
step 26: 1323409263243363903332
+ 2333093633423629043231
step 27: 3656502896666992946563
+ 3656492996666982056563
step 28: 7312995893333975003126
+ 6213005793333985992137
step 29: 13526001686667960995263
+ 36259906976668610062531
step 30: 49785908663336571057794
+ 49775017563336680958794
step 31: 99560926226673252016588
+ 88561025237662262906599
step 32: 188121951464335514923187
+ 781329415533464159121881
step 33: 969451366997799674045068
+ 860540476997799663154969
step 34: 1829991843995599337200037
+ 7300027339955993481999281
step 35: 9130019183951592819199318
+ 8139919182951593819100319
step 36: 17269938366903186638299637
+ 73699283668130966383996271
step 37: 90969222035034153022295908
+ 80959222035143053022296909
step 38: 171928444070177206044592817
+ 718295440602771070444829171
step 39: 890223884672948276489421988
+ 889124984672849276488322098
step 40: 1779348869345797552977744086
+ 6804477792557975439688439771
step 41: 8583826661903772992666183857
+ 7583816662992773091666283858
step 42: 16167643324896546084332467715
+ 51776423348064569842334676161
step 43: 67944066672961115926667143876
+ 67834176662951116927666044976
step 44: 135778243335912232854333188852
+ 258881333458232219533342877531
step 45: 394659576794144452387676066383
+ 383660676783254441497675956493
step 46: 778320253577398893885352022876
+ 678220253588398893775352023877
step 47: 1456540507165797787660704046753
+ 3576404070667877975617050456541
step 48: 5032944577833675763277754503294
+ 4923054577723675763387754492305
step 49: 9955999155557351526665508995599
+ 9955998055666251537555519995599
step 50: 19911997211223603064221028991198
+ 89119982012246030632211279911991
step 51: 109031979223469633696432308903189
+ 981309803234696336964322979130901
step 52: 1090341782458165970660755288034090
+ 0904308825570660795618542871430901
step 53: 1994650608028826766279298159464991
+ 1994649518929726676288208060564991
step 54: 3989300126958553442567506220029982
+ 2899200226057652443558596210039893
step 55: 6888500353016205886126102430069875
+ 5789600342016216885026103530058886
step 56: 12678100695032422771152205960128761
+ 16782106950225117722423059600187621
step 57: 29460207645257540493575265560316382
+ 28361306556257539404575254670206492
step 58: 57821514201515079898150520230522874
+ 47822503202505189897051510241512875
step 59: 105644017404020269795202030472035749
+ 947530274030202597962020404710446501
step 60: 1053174291434222867757222435182482250
+ 0522842815342227577682224341924713501
step 61: 1576017106776450445439446777107195751
+ 1575917017776449345440546776017106751
step 62: 3151934124552899790879993553124302502
+ 2052034213553999780979982554214391513
step 63: 5203968338106899571859976107338694015
+ 5104968337016799581759986018338693025
step 64: 10308936675123699153619962125677387040
+ 04078377652126991635199632157663980301
step 65: 14387314327250690788819594283341367341
+ 14376314338249591888709605272341378341
step 66: 28763628665500282677529199555682745682
+ 28654728655599192577628200556682636782
step 67: 57418357321099475255157400112365382464
+ 46428356321100475155257499012375381475
step 68: 103846713642199950410414899124740763939
+ 939367047421998414014059991246317648301
step 69: 1043213761064198364424474890371058412240
+ 0422148501730984744244638914601673123401
step 70: 1465362262795183108669113804972731535641
+ 1465351372794083119668013815972622635641
step 71: 2930713635589266228337127620945354171282
+ 2821714535490267217338226629855363170392
step 72: 5752428171079533445675354250800717341674
+ 4761437170080524535765443359701718242575
step 73: 10513865341160057981440797610502435584249
+ 94248553420501679704418975006114356831501
step 74: 104762418761661737685859772616616792415750
+ 057514297616616277958586737166167814267401
step 75: 162276716378278015644446509782784606683151
+ 151386606487287905644446510872873617672261
step 76: 313663322865565921288893020655658224355412
+ 214553422856556020398882129565568223366313
step 77: 528216745722121941687775150221226447721725
+ 527127744622122051577786149121227547612825
step 78: 1055344490344243993265561299342453995334550
+ 0554335993542439921655623993424430944435501
step 79: 1609680483886683914921185292766884939770051
+ 1500779394886672925811294193866883840869061
step 80: 3110459878773356840732479486633768780639112
+ 2119360878673366849742370486533778789540113
step 81: 5229820757446723690474849973167547570179225
+ 5229710757457613799484740963276447570289225
step 82: 10459531514904337489959590936443995140468450
+ 05486404159934463909595998473340941513595401
step 83: 15945935674838801399555589409784936654063851
+ 15836045663948790498555599310883847653954951
step 84: 31781981338787591898111188720668784308018802
+ 20881080348786602788111189819578783318918713
step 85: 52663061687574194686222378540247567626937515
+ 51573962676574204587322268649147578616036625
step 86: 104237024364148399273544647189395146242974140
+ 041479242641593981746445372993841463420732401
step 87: 145716267005742381019990020183236609663706541
+ 145607366906632381020099910183247500762617541
step 88: 291323633912374762040089930366484110426324082
+ 280423624011484663039980040267473219336323192
step 89: 571747257923859425080069970633957329762647274
+ 472746267923759336079960080524958329752747175
step 90: 1044493525847618761160030051158915659515394449
+ 9444935159565198511500300611678167485253944401
step 91: 10489428685412817272660330662837083144769338850
+ 05883396744138073826603306627271821458682498401
step 92: 16372825429550891099263637290108904603451837251
+ 15273815430640980109273636299019805592452827361
step 93: 31646640860191871208537273589128710195904664612
+ 21646640959101782198537273580217819106804664613
step 94: 53293281819293653407074547169346529302709329225
+ 52292390720392564396174547070435639291818239235
step 95: 105585672539686217803249094239782168594527568460
+ 064865725495861287932490942308712686935276585501
step 96: 170451398035547505735740036548494855529804153961
+ 169351408925558494845630047537505745530893154071
step 97: 339802806961106000581370084086000601060697308032
+ 230803796060106000680480073185000601169608208933
step 98: 570606603021212001261850157271001202230305516965
+ 569615503032202100172751058162100212120306606075
step 99: 1140222106053414101434601215433101414350612123040
+ 0403212160534141013345121064341014143506012220411
step 100: 1543434266587555114779722279774115557856624343451
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7007009909 takes 100 iterations / steps to resolve into a 49 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 2,549,959 times since Saturday, March 9th, 2002.)
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