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REVERSAL-ADDITION
PALINDROME
TEST ON
1050027948
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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 1050027948: |
1050027948
+ 8497200501
step 1: 9547228449
+ 9448227459
step 2: 18995455908
+ 80955459981
step 3: 99950915889
+ 98851905999
step 4: 198802821888
+ 888128208891
step 5: 1086931030779
+ 9770301396801
step 6: 10857232427580
+ 08572423275801
step 7: 19429655703381
+ 18330755692491
step 8: 37760411395872
+ 27859311406773
step 9: 65619722802645
+ 54620822791656
step 10: 120240545594301
+ 103495545042021
step 11: 223736090636322
+ 223636090637322
step 12: 447372181273644
+ 446372181273744
step 13: 893744362547388
+ 883745263447398
step 14: 1777489625994786
+ 6874995269847771
step 15: 8652484895842557
+ 7552485984842568
step 16: 16204970880685125
+ 52158608807940261
step 17: 68363579688625386
+ 68352688697536386
step 18: 136716268386161772
+ 277161683862617631
step 19: 413877952248779403
+ 304977842259778314
step 20: 718855794508557717
+ 717755805497558817
step 21: 1436611600006116534
+ 4356116000061166341
step 22: 5792727600067282875
+ 5782827600067272975
step 23: 11575555200134555850
+ 05855543100255557511
step 24: 17431098300390113361
+ 16331109300389013471
step 25: 33762207600779126832
+ 23862197700670226733
step 26: 57624405301449353565
+ 56535394410350442675
step 27: 114159799711799796240
+ 042697997117997951411
step 28: 156857796829797747651
+ 156747797928697758651
step 29: 313605594758495506302
+ 203605594857495506313
step 30: 517211189615991012615
+ 516210199516981112715
step 31: 1033421389132972125330
+ 0335212792319831243301
step 32: 1368634181452803368631
+ 1368633082541814368631
step 33: 2737267263994617737262
+ 2627377164993627627372
step 34: 5364644428988245364634
+ 4364635428898244464635
step 35: 9729279857886489829269
+ 9629289846887589729279
step 36: 19358569704774079558548
+ 84585597047740796585391
step 37: 103944166752514876143939
+ 939341678415257661449301
step 38: 1043285845167772537593240
+ 0423957352777615485823401
step 39: 1467243197945388023416641
+ 1466143208835497913427641
step 40: 2933386406780885936844282
+ 2824486395880876046833392
step 41: 5757872802661761983677674
+ 4767763891671662082787575
step 42: 10525636694333424066465249
+ 94256466042433349663652501
step 43: 104782102736766773730117750
+ 057711037377667637201287401
step 44: 162493140114434410931405151
+ 151504139014434411041394261
step 45: 313997279128868821972799412
+ 214997279128868821972799313
step 46: 528994558257737643945598725
+ 527895549346737752855499825
step 47: 1056890107604475396801098550
+ 0558901086935744067010986501
step 48: 1615791194540219463812085051
+ 1505802183649120454911975161
step 49: 3121593378189339918724060212
+ 2120604278199339818733951213
step 50: 5242197656388679737458011425
+ 5241108547379768836567912425
step 51: 10483306203768448574025923850
+ 05832952047584486730260338401
step 52: 16316258251352935304286262251
+ 15226268240353925315285261361
step 53: 31542526491706860619571523612
+ 21632517591606860719462524513
step 54: 53175044083313721339034048125
+ 52184043093312731338044057135
step 55: 105359087176626452677078105260
+ 062501870776254626671780953501
step 56: 167860957952881079348859058761
+ 167850958843970188259759068761
step 57: 335711916796851267608618127522
+ 225721816806762158697619117533
step 58: 561433733603613426306237245055
+ 550542732603624316306337334165
step 59: 1111976466207237742612574579220
+ 0229754752162477327026646791111
step 60: 1341731218369715069639221370331
+ 1330731229369605179638121371431
step 61: 2672462447739320249277342741762
+ 2671472437729420239377442642762
step 62: 5343934885468740488654785384524
+ 4254835874568840478645884393435
step 63: 9598770760037580967300669777959
+ 9597779660037690857300670778959
step 64: 19196550420075271824601340556918
+ 81965504310642817257002405569191
step 65: 101162054730718089081603746126109
+ 901621647306180980817037450261101
step 66: 1002783702036899069898641196387210
+ 0127836911468989609986302073872001
step 67: 1130620613505888679884943270259211
+ 1129520723494889768885053160260311
step 68: 2260141337000778448769996430519522
+ 2259150346999678448770007331410622
step 69: 4519291684000456897540003761930144
+ 4410391673000457986540004861929154
step 70: 8929683357000914884080008623859298
+ 8929583268000804884190007533869298
step 71: 17859266625001719768270016157728596
+ 69582775161007286791710052666295871
step 72: 87442041786009006559980068824024467
+ 76442042886008995560090068714024478
step 73: 163884084672018002120070137538048945
+ 549840835731070021200810276480488361
step 74: 713724920403088023320880414018537306
+ 603735810414088023320880304029427317
step 75: 1317460730817176046641760718047964623
+ 3264697408170671466406717180370647131
step 76: 4582158138987847513048477898418611754
+ 4571168148987748403157487898318512854
step 77: 9153326287975595916205965796737124608
+ 8064217376975695026195955797826233519
step 78: 17217543664951290942401921594563358127
+ 72185336549512910424909215946634571271
step 79: 89402880214464201367311137541197929398
+ 89392979114573111376310246441208820498
step 80: 178795859329037312743621383982406749896
+ 698947604289383126347213730923958597871
step 81: 877743463618420439090835114906365347767
+ 767743563609411538090934024816364347778
step 82: 1645487027227831977181769139722729695545
+ 5455969272279319671817791387227207845461
step 83: 7101456299507151648999560526949937541006
+ 6001457399496250659998461517059926541017
step 84: 13102913699003402308998022044009864082023
+ 32028046890044022089980320430099631920131
step 85: 45130960589047424398978342474109496002154
+ 45120069490147424387989342474098506903154
step 86: 90251030079194848786967684948208002905308
+ 80350920080284948676968784849197003015209
step 87: 170601950159479797463936469797405005920517
+ 715029500504797964639364797974951059106071
step 88: 885631450664277762103301267772356065026588
+ 885620560653277762103301267772466054136588
step 89: 1771252011317555524206602535544822119163176
+ 6713619112284455352066024255557131102521771
step 90: 8484871123602010876272626791101953221684947
+ 7494861223591011976262726780102063211784848
step 91: 15979732347193022852535353571204016433469795
+ 59796433461040217535353525822039174323797951
step 92: 75776165808233240387888879393243190757267746
+ 64776275709134239397888878304233280856167757
step 93: 140552441517367479785777757697476471613435503
+ 305534316174674796757777587974763715144255041
step 94: 446086757692042276543555345672240186757690544
+ 445096757681042276543555345672240296757680644
step 95: 891183515373084553087110691344480483515371188
+ 881173515384084443196011780355480373515381198
step 96: 1772357030757168996283122471699960857030752386
+ 6832570307580699961742213826998617570307532771
step 97: 8604927338337868958025336298698578427338285157
+ 7515828337248758968926335208598687338337294068
step 98: 16120755675586627926951671507297265765675579225
+ 52297557656756279270517615962972668557655702161
step 99: 68418313332342907197469287470269934323331281386
+ 68318213332343996207478296479170924323331381486
step 100: 136736526664686903404947583949440858646662662872
+ 278266266646858044949385749404309686466625637631
step 101: 415002793311544948354333333353750545113288300503
+ 305003882311545057353333333453849445113397200514
step 102: 720006675623090005707666666807599990226685501017
+ 710105586622099995708666666707500090326576600027
step 103: 1430112262245190001416333333515100080553262101044
+ 4401012623550800015153333336141000915422622110341
step 104: 5831124885795990016569666669656100995975884211385
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1050027948 takes 104 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 2,542,457 times since Saturday, March 9th, 2002.)
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