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REVERSAL-ADDITION
PALINDROME
TEST ON
1000005469548
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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 1000005469548: |
1000005469548
+ 8459645000001
step 1: 9459650469549
+ 9459640569549
step 2: 18919291039098
+ 89093019291981
step 3: 108012310331079
+ 970133013210801
step 4: 1078145323541880
+ 0881453235418701
step 5: 1959598558960581
+ 1850698558959591
step 6: 3810297117920172
+ 2710297117920183
step 7: 6520594235840355
+ 5530485324950256
step 8: 12051079560790611
+ 11609706597015021
step 9: 23660786157805632
+ 23650875168706632
step 10: 47311661326512264
+ 46221562316611374
step 11: 93533223643123638
+ 83632134632233539
step 12: 177165358275357177
+ 771753572853561771
step 13: 948918931128918948
+ 849819821139819849
step 14: 1798738752268738797
+ 7978378622578378971
step 15: 9777117374847117768
+ 8677117484737117779
step 16: 18454234859584235547
+ 74553248595843245481
step 17: 93007483455427481028
+ 82018472455438470039
step 18: 175025955910865951067
+ 760159568019559520571
step 19: 935185523930425471638
+ 836174524039325581539
step 20: 1771360047969751053177
+ 7713501579697400631771
step 21: 9484861627667151684948
+ 8494861517667261684849
step 22: 17979723145334413369797
+ 79796331443354132797971
step 23: 97776054588688546167768
+ 86776164588688545067779
step 24: 184552219177377091235547
+ 745532190773771912255481
step 25: 930084409951149003491028
+ 820194300941159904480039
step 26: 1750278710892308907971067
+ 7601797098032980178720571
step 27: 9352075808925289086691638
+ 8361966809825298085702539
step 28: 17714042618750587172394177
+ 77149327178505781624041771
step 29: 94863369797256368796435948
+ 84953469786365279796336849
step 30: 179816839583621648592772797
+ 797277295846126385938618971
step 31: 977094135429748034531391768
+ 867193135430847924531490779
step 32: 1844287270860595959062882547
+ 7452882609595950680727824481
step 33: 9297169880456546639790707028
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step 34: 17504240859823003180680324957
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step 35: 93446549467953036076484565528
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step 36: 176003097935016072052979129967
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step 37: 945925077185286682592769430638
+ 836034967295286682581770529549
step 38: 1781960044480573365174539960187
+ 7810699354715633750844400691871
step 39: 9592659399196207116018940652058
+ 8502560498106117026919939562959
step 40: 18095219897302324142938880215017
+ 71051208883924142320379891259081
step 41: 89146428781226466463318771474098
+ 89047417781336466462218782464198
step 42: 178193846562562932925537553938296
+ 692839355735529239265265648391871
step 43: 871033202298092172190803202330167
+ 761033202308091271290892202330178
step 44: 1632066404606183443481695404660345
+ 5430664045961843443816064046602361
step 45: 7062730450568026887297759451262706
+ 6072621549577927886208650540372607
step 46: 13135352000145954773506409991635313
+ 31353619990460537745954100025353131
step 47: 44488971990606492519460510016988444
+ 44488961001506491529460609917988444
step 48: 88977932992112984048921119934976888
+ 88867943991112984048921129923977988
step 49: 177845876983225968097842249858954876
+ 678459858942248790869522389678548771
step 50: 856305735925474758967364639537503647
+ 746305735936463769857474529537503658
step 51: 1602611471861938528824839169075007305
+ 5037005709619384288258391681741162061
step 52: 6639617181481322817083230850816169366
+ 6639616180580323807182231841817169366
step 53: 13279233362061646624265462692633338732
+ 23783333629626456242664616026333297231
step 54: 37062566991688102866930078718966635963
+ 36953666981787003966820188619966526073
step 55: 74016233973475106833750267338933162036
+ 63026133983376205733860157437933261047
step 56: 137042367956851312567610424776866423083
+ 380324668677424016765213158659763240731
step 57: 517367036634275329332823583436629663814
+ 418366926634385328233923572436630763715
step 58: 935733963268660657566747155873260427529
+ 925724062378551747665756066862369337539
step 59: 1861458025647212405232503222735629765068
+ 8605679265372223052325042127465208541681
step 60: 10467137291019435457557545350200838306749
+ 94760383800205354575575453491019273176401
step 61: 105227521091224790033132998841220111483150
+ 051384111022148899231330097422190125722501
step 62: 156611632113373689264463096263410237205651
+ 156502732014362690364462986373311236116651
step 63: 313114364127736379628926082636721473322302
+ 203223374127636280629826973637721463411313
step 64: 516337738255372660258753056274442936733615
+ 516337639244472650357852066273552837733615
step 65: 1032675377499845310616605122547995774467230
+ 0327644775997452215066160135489947735762301
step 66: 1360320153497297525682765258037943510229531
+ 1359220153497308525672865257927943510230631
step 67: 2719540306994606051355630515965887020460162
+ 2610640207885695150365531506064996030459172
step 68: 5330180514880301201721162022030883050919334
+ 4339190503880302202611271021030884150810335
step 69: 9669371018760603404332433043061767201729669
+ 9669271027671603403342334043060678101739669
step 70: 19338642046432206807674767086122445303469338
+ 83396430354422168076747670860223464024683391
step 71: 102735072400854374884422437946345909328152729
+ 927251823909543649734224488473458004270537201
step 72: 1029986896310398024618646926419803913598689930
+ 0399868953193089146296468164208930136986899201
step 73: 1429855849503487170915115090628734050585589131
+ 1319855850504378260905115190717843059485589241
step 74: 2749711700007865431820230281346577110071178372
+ 2738711700117756431820320281345687000071179472
step 75: 5488423400125621863640550562692264110142357844
+ 4487532410114622962650550463681265210043248845
step 76: 9975955810240244826291101026373529320185606689
+ 9866065810239253736201011926284420420185595799
step 77: 19842021620479498562492112952657949740371202488
+ 88420217304794975625921129426589497402612024891
step 78: 108262238925274474188413242379247447142983227379
+ 973722389241744742973242314881474472529832262801
step 79: 1081984628167019217161655557260721919672815490180
+ 0810945182769191270627555561617129107618264891801
step 80: 1892929810936210487789211118877851027291080381981
+ 1891830801927201587788111129877840126390189292981
step 81: 3784760612863412075577322248755691153681269674962
+ 2694769621863511965578422237755702143682160674873
step 82: 6479530234726924041155744486511393297363430349835
+ 5389430343637923931156844475511404296274320359746
step 83: 11868960578364847972312588962022797593637750709581
+ 18590705773639579722026988521327974846387506986811
step 84: 30459666352004427694339577483350772440025257696392
+ 29369675252004427705338477593349672440025366695403
step 85: 59829341604008855399678055076700444880050624391795
+ 59719342605008844400767055087699355880040614392895
step 86: 119548684209017699800445110164399800760091238784690
+ 096487832190067008993461011544008996710902486845911
step 87: 216036516399084708793906121708408797470993725630601
+ 106036527399074797804807121609397807480993615630612
step 88: 322073043798159506598713243317806604951987341261213
+ 312162143789159406608713342317895605951897340370223
step 89: 634235187587318913207426585635702210903884681631436
+ 634136186488309012207536585624702319813785781532436
step 90: 1268371374075627925414963171260404530717670463163872
+ 2783613640767170354040621713694145297265704731738621
step 91: 4051985014842798279455584884954549827983375194902493
+ 3942094915733897289454594884855549728972484105891504
step 92: 7994079930576695568910179769810099556955859300793997
+ 7993970039585596559900189679710198655966750399704997
step 93: 15988049970162292128810369449520298212922609700498994
+ 49989400790622921289202594496301882129226107994088951
step 94: 65977450760785213418012963945822180342148717694587945
+ 54978549671784124308122854936921081431258706705477956
step 95: 120956000432569337726135818882743261773407424400065901
+ 109560004424704377162347288818531627733965234000659021
step 96: 230516004857273714888483107701274889507372658400724922
+ 229427004856273705988472107701384888417372758400615032
step 97: 459943009713547420876955215402659777924745416801339954
+ 459933108614547429777956204512559678024745317900349954
step 98: 919876118328094850654911419915219455949490734701689908
+ 809986107437094949554912519914119456058490823811678919
step 99: 1729862225765189800209823939829338912007981558513368827
+ 7288633158551897002198339289393289020089815675222689271
step 100: 9018495384317086802408163229222627932097797233736058098
+ 8908506373327977902397262229223618042086807134835948109
step 101: 17927001757645064704805425458446245974184604368572006207
+ 70260027586340648147954264485452450840746054675710072971
step 102: 88187029343985712852759689943898696814930659044282079178
+ 87197028244095603941869689834998695725821758934392078188
step 103: 175384057588081316794629379778897392540752417978674157366
+ 663751476879714257045293798877973926497613180885750483571
step 104: 839135534467795573839923178656871319038365598864424640937
+ 739046424468895563830913178656871329938375597764435531938
step 105: 1578181958936691137670836357313742648976741196628860172875
+ 5782710688266911476798462473137536380767311966398591818751
step 106: 7360892647203602614469298830451279029744053163027451991626
+ 6261991547203613504479209721540388929644162063027462980637
step 107: 13622884194407216118948508551991667959388215226054914972263
+ 36227941945062251288395976619915580584981161270449148822631
step 108: 49850826139469467407344485171907248544369376496504063794894
+ 49849736040569467396344584270917158444370476496493162805894
step 109: 99700562180038934803689069442824406988739852992997226600788
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step 110: 188401224459968860697478029885648903087370696976005353101587
+ 785101353500679696073780309846588920874796068869954422104881
step 111: 973502577960648556771258339732237823962166765845959775206468
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step 112: 1838105155920197124432527668464475757814344421692029550411847
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step 113: 9319245715123158368866715244209124425066688639602325065430228
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step 114: 17539591320355227737733320488428148850243377278115540240859367
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step 115: 93935395524906415015067526372610637252577151050370842560452938
+ 83925406524807305015177525273601627362576051051460942559353939
step 116: 177860802049713720030245051646212264615153202101831785119806877
+ 778608911587138101202351516462212646150542030027317940208068771
step 117: 956469713636851821232596568108424910765695232129149725327875648
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step 118: 1803048437164793742465193135127849712631390464257308361645840307
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step 119: 8833533898802831267106124497307336927945306106731282978994243388
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step 120: 17666958897595652643122159994603673965889522124352665067977596776
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step 121: 85436536873652277985244758851541304615884644258978324647863563447
+ 74436536874642387985244648851640314515885744258977225637863563458
step 122: 159873073748294665970489407703181619131770388517955550285727126905
+ 509621727582055559715883077131916181307704984079566492847370378951
step 123: 669494801330350225686372484835097800439475372597522043133097505856
+ 658505790331340225795273574934008790538484273686522053033108494966
step 124: 1328000591661690451481646059769106590977959646284044096166206000822
+ 2280006026616904404826469597790956019679506461841540961661950008231
step 125: 3608006618278594856308115657560062610657466108125585057828156009053
+ 3509006518287505855218016647560162600657565118036584958728166008063
step 126: 7117013136566100711526132305120225211315031226162170016556322017116
+ 6117102236556100712616221305131125220215032316251170016656313107117
step 127: 13234115373122201424142353610251350431530063542413340033212635124233
+ 33242153621233004331424536003513405315201635324142410222137351143231
step 128: 46476268994355205755566889613764755746731698866555750255349986267464
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1000005469548 takes 128 iterations / steps to resolve into a 68 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
|
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] |
|---|
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 2,497,318 times since Saturday, March 9th, 2002.)
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