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REVERSAL-ADDITION
PALINDROME
TEST ON
1304199693
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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 1304199693: |
1304199693
+ 3969914031
step 1: 5274113724
+ 4273114725
step 2: 9547228449
+ 9448227459
step 3: 18995455908
+ 80955459981
step 4: 99950915889
+ 98851905999
step 5: 198802821888
+ 888128208891
step 6: 1086931030779
+ 9770301396801
step 7: 10857232427580
+ 08572423275801
step 8: 19429655703381
+ 18330755692491
step 9: 37760411395872
+ 27859311406773
step 10: 65619722802645
+ 54620822791656
step 11: 120240545594301
+ 103495545042021
step 12: 223736090636322
+ 223636090637322
step 13: 447372181273644
+ 446372181273744
step 14: 893744362547388
+ 883745263447398
step 15: 1777489625994786
+ 6874995269847771
step 16: 8652484895842557
+ 7552485984842568
step 17: 16204970880685125
+ 52158608807940261
step 18: 68363579688625386
+ 68352688697536386
step 19: 136716268386161772
+ 277161683862617631
step 20: 413877952248779403
+ 304977842259778314
step 21: 718855794508557717
+ 717755805497558817
step 22: 1436611600006116534
+ 4356116000061166341
step 23: 5792727600067282875
+ 5782827600067272975
step 24: 11575555200134555850
+ 05855543100255557511
step 25: 17431098300390113361
+ 16331109300389013471
step 26: 33762207600779126832
+ 23862197700670226733
step 27: 57624405301449353565
+ 56535394410350442675
step 28: 114159799711799796240
+ 042697997117997951411
step 29: 156857796829797747651
+ 156747797928697758651
step 30: 313605594758495506302
+ 203605594857495506313
step 31: 517211189615991012615
+ 516210199516981112715
step 32: 1033421389132972125330
+ 0335212792319831243301
step 33: 1368634181452803368631
+ 1368633082541814368631
step 34: 2737267263994617737262
+ 2627377164993627627372
step 35: 5364644428988245364634
+ 4364635428898244464635
step 36: 9729279857886489829269
+ 9629289846887589729279
step 37: 19358569704774079558548
+ 84585597047740796585391
step 38: 103944166752514876143939
+ 939341678415257661449301
step 39: 1043285845167772537593240
+ 0423957352777615485823401
step 40: 1467243197945388023416641
+ 1466143208835497913427641
step 41: 2933386406780885936844282
+ 2824486395880876046833392
step 42: 5757872802661761983677674
+ 4767763891671662082787575
step 43: 10525636694333424066465249
+ 94256466042433349663652501
step 44: 104782102736766773730117750
+ 057711037377667637201287401
step 45: 162493140114434410931405151
+ 151504139014434411041394261
step 46: 313997279128868821972799412
+ 214997279128868821972799313
step 47: 528994558257737643945598725
+ 527895549346737752855499825
step 48: 1056890107604475396801098550
+ 0558901086935744067010986501
step 49: 1615791194540219463812085051
+ 1505802183649120454911975161
step 50: 3121593378189339918724060212
+ 2120604278199339818733951213
step 51: 5242197656388679737458011425
+ 5241108547379768836567912425
step 52: 10483306203768448574025923850
+ 05832952047584486730260338401
step 53: 16316258251352935304286262251
+ 15226268240353925315285261361
step 54: 31542526491706860619571523612
+ 21632517591606860719462524513
step 55: 53175044083313721339034048125
+ 52184043093312731338044057135
step 56: 105359087176626452677078105260
+ 062501870776254626671780953501
step 57: 167860957952881079348859058761
+ 167850958843970188259759068761
step 58: 335711916796851267608618127522
+ 225721816806762158697619117533
step 59: 561433733603613426306237245055
+ 550542732603624316306337334165
step 60: 1111976466207237742612574579220
+ 0229754752162477327026646791111
step 61: 1341731218369715069639221370331
+ 1330731229369605179638121371431
step 62: 2672462447739320249277342741762
+ 2671472437729420239377442642762
step 63: 5343934885468740488654785384524
+ 4254835874568840478645884393435
step 64: 9598770760037580967300669777959
+ 9597779660037690857300670778959
step 65: 19196550420075271824601340556918
+ 81965504310642817257002405569191
step 66: 101162054730718089081603746126109
+ 901621647306180980817037450261101
step 67: 1002783702036899069898641196387210
+ 0127836911468989609986302073872001
step 68: 1130620613505888679884943270259211
+ 1129520723494889768885053160260311
step 69: 2260141337000778448769996430519522
+ 2259150346999678448770007331410622
step 70: 4519291684000456897540003761930144
+ 4410391673000457986540004861929154
step 71: 8929683357000914884080008623859298
+ 8929583268000804884190007533869298
step 72: 17859266625001719768270016157728596
+ 69582775161007286791710052666295871
step 73: 87442041786009006559980068824024467
+ 76442042886008995560090068714024478
step 74: 163884084672018002120070137538048945
+ 549840835731070021200810276480488361
step 75: 713724920403088023320880414018537306
+ 603735810414088023320880304029427317
step 76: 1317460730817176046641760718047964623
+ 3264697408170671466406717180370647131
step 77: 4582158138987847513048477898418611754
+ 4571168148987748403157487898318512854
step 78: 9153326287975595916205965796737124608
+ 8064217376975695026195955797826233519
step 79: 17217543664951290942401921594563358127
+ 72185336549512910424909215946634571271
step 80: 89402880214464201367311137541197929398
+ 89392979114573111376310246441208820498
step 81: 178795859329037312743621383982406749896
+ 698947604289383126347213730923958597871
step 82: 877743463618420439090835114906365347767
+ 767743563609411538090934024816364347778
step 83: 1645487027227831977181769139722729695545
+ 5455969272279319671817791387227207845461
step 84: 7101456299507151648999560526949937541006
+ 6001457399496250659998461517059926541017
step 85: 13102913699003402308998022044009864082023
+ 32028046890044022089980320430099631920131
step 86: 45130960589047424398978342474109496002154
+ 45120069490147424387989342474098506903154
step 87: 90251030079194848786967684948208002905308
+ 80350920080284948676968784849197003015209
step 88: 170601950159479797463936469797405005920517
+ 715029500504797964639364797974951059106071
step 89: 885631450664277762103301267772356065026588
+ 885620560653277762103301267772466054136588
step 90: 1771252011317555524206602535544822119163176
+ 6713619112284455352066024255557131102521771
step 91: 8484871123602010876272626791101953221684947
+ 7494861223591011976262726780102063211784848
step 92: 15979732347193022852535353571204016433469795
+ 59796433461040217535353525822039174323797951
step 93: 75776165808233240387888879393243190757267746
+ 64776275709134239397888878304233280856167757
step 94: 140552441517367479785777757697476471613435503
+ 305534316174674796757777587974763715144255041
step 95: 446086757692042276543555345672240186757690544
+ 445096757681042276543555345672240296757680644
step 96: 891183515373084553087110691344480483515371188
+ 881173515384084443196011780355480373515381198
step 97: 1772357030757168996283122471699960857030752386
+ 6832570307580699961742213826998617570307532771
step 98: 8604927338337868958025336298698578427338285157
+ 7515828337248758968926335208598687338337294068
step 99: 16120755675586627926951671507297265765675579225
+ 52297557656756279270517615962972668557655702161
step 100: 68418313332342907197469287470269934323331281386
+ 68318213332343996207478296479170924323331381486
step 101: 136736526664686903404947583949440858646662662872
+ 278266266646858044949385749404309686466625637631
step 102: 415002793311544948354333333353750545113288300503
+ 305003882311545057353333333453849445113397200514
step 103: 720006675623090005707666666807599990226685501017
+ 710105586622099995708666666707500090326576600027
step 104: 1430112262245190001416333333515100080553262101044
+ 4401012623550800015153333336141000915422622110341
step 105: 5831124885795990016569666669656100995975884211385
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1304199693 takes 105 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 2,549,923 times since Saturday, March 9th, 2002.)
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