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REVERSAL-ADDITION
PALINDROME
TEST ON
1090001921
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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 1090001921: |
1090001921
+ 1291000901
step 1: 2381002822
+ 2282001832
step 2: 4663004654
+ 4564003664
step 3: 9227008318
+ 8138007229
step 4: 17365015547
+ 74551056371
step 5: 91916071918
+ 81917061919
step 6: 173833133837
+ 738331338371
step 7: 912164472208
+ 802274461219
step 8: 1714438933427
+ 7243398344171
step 9: 8957837277598
+ 8957727387598
step 10: 17915564665196
+ 69156646551971
step 11: 87072211217167
+ 76171211227078
step 12: 163243422444245
+ 542444224342361
step 13: 705687646786606
+ 606687646786507
step 14: 1312375293573113
+ 3113753925732131
step 15: 4426129219305244
+ 4425039129216244
step 16: 8851168348521488
+ 8841258438611588
step 17: 17692426787133076
+ 67033178762429671
step 18: 84725605549562747
+ 74726594550652748
step 19: 159452200100215495
+ 594512001002254951
step 20: 753964201102470446
+ 644074201102469357
step 21: 1398038402204939803
+ 3089394022048308931
step 22: 4487432424253248734
+ 4378423524242347844
step 23: 8865855948495596578
+ 8756955948495585688
step 24: 17622811896991182266
+ 66228119969811822671
step 25: 83850931866803004937
+ 73940030866813905838
step 26: 157790962733616910775
+ 577019616337269097751
step 27: 734810579070886008526
+ 625800688070975018437
step 28: 1360611267141861026963
+ 3696201681417621160631
step 29: 5056812948559482187594
+ 4957812849558492186505
step 30: 10014625798117974374099
+ 99047347971189752641001
step 31: 109061973769307727015100
+ 001510727703967379160901
step 32: 110572701473275106176001
+ 100671601572374107275011
step 33: 211244303045649213451012
+ 210154312946540303442112
step 34: 421398615992189516893124
+ 421398615981299516893124
step 35: 842797231973489033786248
+ 842687330984379132797248
step 36: 1685484562957868166583496
+ 6943856618687592654845861
step 37: 8629341181645460821429357
+ 7539241280645461811439268
step 38: 16168582462290922632868625
+ 52686823622909226428586161
step 39: 68855406085200149061454786
+ 68745416094100258060455886
step 40: 137600822179300407121910672
+ 276019121704003971228006731
step 41: 413619943883304378349917403
+ 304719943873403388349916314
step 42: 718339887756707766699833717
+ 717338996667707657788933817
step 43: 1435678884424415424488767534
+ 4357678844245144244888765341
step 44: 5793357728669559669377532875
+ 5782357739669559668277533975
step 45: 11575715468339119337655066850
+ 05866055673391193386451757511
step 46: 17441771141730312724106824361
+ 16342860142721303714117714471
step 47: 33784631284451616438224538832
+ 23883542283461615448213648733
step 48: 57668173567913231886438187565
+ 56578183468813231976537186675
step 49: 114246357036726463862975374240
+ 042473579268364627630753642411
step 50: 156719936305091091493729016651
+ 156610927394190190503639917651
step 51: 313330863699281281997368934302
+ 203439863799182182996368033313
step 52: 516770727498463464993736967615
+ 516769637399464364894727077615
step 53: 1033540364897927829888464045230
+ 0325404648889287297984630453301
step 54: 1358945013787215127873094498531
+ 1358944903787215127873105498531
step 55: 2717889917574430255746199997062
+ 2607999916475520344757199887172
step 56: 5325889834049950600503399884234
+ 4324889933050060599404389885235
step 57: 9650779767100011199907789769469
+ 9649679877099911100017679770569
step 58: 19300459644199922299925469540038
+ 83004596452999222999144695400391
step 59: 102305056097199145299070164940429
+ 924049461070992541991790650503201
step 60: 1026354517168191687290860815443630
+ 0363445180680927861918617154536201
step 61: 1389799697849119549209477969979831
+ 1389799697749029459119487969979831
step 62: 2779599395598149008328965939959662
+ 2669599395698238009418955939959772
step 63: 5449198791296387017747921879919434
+ 4349199781297477107836921978919445
step 64: 9798398572593864125584843858838879
+ 9788388583484855214683952758938979
step 65: 19586787156078719340268796617777858
+ 85877771669786204391787065178768591
step 66: 105464558825864923732055861796546449
+ 944645697168550237329468528855464501
step 67: 1050110255994415161061524390652010950
+ 0590102560934251601615144995520110501
step 68: 1640212816928666762676669386172121451
+ 1541212716839666762676668296182120461
step 69: 3181425533768333525353337682354241912
+ 2191424532867333535253338673355241813
step 70: 5372850066635667060606676355709483725
+ 5273849075536766060607665366600582735
step 71: 10646699142172433121214341722310066460
+ 06466001322714341212133427124199664601
step 72: 17112700464886774333347768846509731061
+ 16013790564886774333347768846400721171
step 73: 33126491029773548666695537692910452232
+ 23225401929673559666684537792019462133
step 74: 56351892959447108333380075484929914365
+ 56341992948457008333380174495929815365
step 75: 112693885907904116666760249980859729730
+ 037927958089942067666611409709588396211
step 76: 150621843997846184333371659690448125941
+ 149521844096956173333481648799348126051
step 77: 300143688094802357666853308489796251992
+ 299152697984803358666753208490886341003
step 78: 599296386079605716333606516980682592995
+ 599295286089615606333617506970683692995
step 79: 1198591672169221322667224023951366285990
+ 0995826631593204227662231229612761958911
step 80: 2194418303762425550329455253564128244901
+ 1094428214653525549230555242673038144912
step 81: 3288846518415951099560010496237166389813
+ 3189836617326940100659901595148156488823
step 82: 6478683135742891200219912091385322878636
+ 6368782235831902199120021982475313868746
step 83: 12847465371574793399339934073860636747382
+ 28374763606837043993399339747517356474821
step 84: 41222228978411837392739273821377993222203
+ 30222239977312837293729373811487982222214
step 85: 71444468955724674686468647632865975444417
+ 71444457956823674686468647642755986444417
step 86: 142888926912548349372937295275621961888834
+ 438888169126572592739273943845219629888241
step 87: 581777096039120942112211239120841591777075
+ 570777195148021932112211249021930690777185
step 88: 1152554291187142874224422488142772282554260
+ 0624552822772418842244224782417811924552511
step 89: 1777107113959561716468647270560584207106771
+ 1776017024850650727468646171659593117017771
step 90: 3553124138810212443937293442220177324124542
+ 2454214237710222443927393442120188314213553
step 91: 6007338376520434887864686884340365638338095
+ 5908338365630434886864687884340256738337006
step 92: 11915676742150869774729374768680622376675101
+ 10157667322608686747392747796805124767651911
step 93: 22073344064759556522122122565485747144327012
+ 21072344174758456522122122565595746044337022
step 94: 43145688239518013044244245131081493188664034
+ 43046688139418013154244244031081593288654134
step 95: 86192376378936026198488489162163086477318168
+ 86181377468036126198488489162063987367329168
step 96: 172373753846972152396976978324227073844647336
+ 633746448370722423879679693251279648357373271
step 97: 806120202217694576276656671575506722202020607
+ 706020202227605575176656672675496712202021608
step 98: 1512140404445300151453313344251003434404042215
+ 5122404044343001524433133541510035444040412151
step 99: 6634544448788301675886446885761038878444454366
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1090001921 takes 99 iterations / steps to resolve into a 46 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 2,499,892 times since Saturday, March 9th, 2002.)
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