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REVERSAL-ADDITION
PALINDROME
TEST ON
5020089949
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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 5020089949: |
5020089949
+ 9499800205
step 1: 14519890154
+ 45109891541
step 2: 59629781695
+ 59618792695
step 3: 119248574390
+ 093475842911
step 4: 212724417301
+ 103714427212
step 5: 316438844513
+ 315448834613
step 6: 631887679126
+ 621976788136
step 7: 1253864467262
+ 2627644683521
step 8: 3881509150783
+ 3870519051883
step 9: 7752028202666
+ 6662028202577
step 10: 14414056405243
+ 34250465041441
step 11: 48664521446684
+ 48664412546684
step 12: 97328933993368
+ 86339933982379
step 13: 183668867975747
+ 747579768866381
step 14: 931248636842128
+ 821248636842139
step 15: 1752497273684267
+ 7624863727942571
step 16: 9377361001626838
+ 8386261001637739
step 17: 17763622003264577
+ 77546230022636771
step 18: 95309852025901348
+ 84310952025890359
step 19: 179620804051791707
+ 707197150408026971
step 20: 886817954459818678
+ 876818954459718688
step 21: 1763636908919537366
+ 6637359198096363671
step 22: 8400996107015901037
+ 7301095107016990048
step 23: 15702091214032891085
+ 58019823041219020751
step 24: 73721914255251911836
+ 63811915255241912737
step 25: 137533829510493824573
+ 375428394015928335731
step 26: 512962223526422160304
+ 403061224625322269215
step 27: 916023448151744429519
+ 915924447151844320619
step 28: 1831947895303588750138
+ 8310578853035987491381
step 29: 10142526748339576241519
+ 91514267593384762524101
step 30: 101656794341724338765620
+ 026567833427143497656101
step 31: 128224627768867836421721
+ 127124638768867726422821
step 32: 255349266537735562844542
+ 245448265537735662943552
step 33: 500797532075471225788094
+ 490887522174570235797005
step 34: 991685054250041461585099
+ 990585164140052450586199
step 35: 1982270218390093912171298
+ 8921712193900938120722891
step 36: 10903982412291032032894189
+ 98149823023019221428930901
step 37: 109053805435310253461825090
+ 090528164352013534508350901
step 38: 199581969787323787970175991
+ 199571079787323787969185991
step 39: 399153049574647575939361982
+ 289163939575746475940351993
step 40: 688316989150394051879713975
+ 579317978150493051989613886
step 41: 1267634967300887103869327861
+ 1687239683017880037694367621
step 42: 2954874650318767141563695482
+ 2845963651417678130564784592
step 43: 5800838301736445272128480074
+ 4700848212725446371038380085
step 44: 10501686514461891643166860159
+ 95106866134619816441568610501
step 45: 105608552649081708084735470660
+ 066074537480807180946255806501
step 46: 171683090129888889030991277161
+ 161772199030988888921090386171
step 47: 333455289160877777952081663332
+ 233366180259777778061982554333
step 48: 566821469420655556014064217665
+ 566712460410655556024964128665
step 49: 1133533929831311112039028346330
+ 0336438209302111131389293353311
step 50: 1469972139133422243428321699641
+ 1469961238243422243319312799641
step 51: 2939933377376844486747634499282
+ 2829944367476844486737733399392
step 52: 5769877744853688973485367898674
+ 4768987635843798863584477789675
step 53: 10538865380697487837069845688349
+ 94388654896073878479608356883501
step 54: 104927520276771366316678202571850
+ 058175202876613663177672025729401
step 55: 163102723153385029494350228301251
+ 152103822053494920583351327201361
step 56: 315206545206879950077701555502612
+ 216205555107770059978602545602513
step 57: 531412100314650010056304101105125
+ 521501101403650010056413001214135
step 58: 1052913201718300020112717102319260
+ 0629132017172110200038171023192501
step 59: 1682045218890410220150888125511761
+ 1671155218880510220140988125402861
step 60: 3353200437770920440291876250914622
+ 2264190526781920440290777340023533
step 61: 5617390964552840880582653590938155
+ 5518390953562850880482554690937165
step 62: 11135781918115691761065208281875320
+ 02357818280256016719651181918753111
step 63: 13493600198371708480716390200628431
+ 13482600209361708480717389100639431
step 64: 26976200407733416961433779301267862
+ 26876210397733416961433770400267962
step 65: 53852410805466833922867549701535824
+ 42853510794576822933866450801425835
step 66: 96705921600043656856734000502961659
+ 95616920500043765865634000612950769
step 67: 192322842100087422722368001115912428
+ 824219511100863227224780001248223291
step 68: 1016542353200950649947148002364135719
+ 9175314632008417499460590023532456101
step 69: 10191856985209368149407738025896591820
+ 02819569852083770494186390258965819101
step 70: 13011426837293138643594128284862410921
+ 12901426848282149534683139273862411031
step 71: 25912853685575288178277267558724821952
+ 25912842785576277287188257558635821952
step 72: 51825696471151565465465525117360643904
+ 40934606371152556456456515117469652815
step 73: 92760302842304121921922040234830296719
+ 91769203843204022912912140324820306729
step 74: 184529506685508144834834180559650603448
+ 844306056955081438438441805586605925481
step 75: 1028835563640589583273275986146256528929
+ 9298256526416895723723859850463655388201
step 76: 10327092090057485306997135836609911917130
+ 03171911990663853179960358475009029072301
step 77: 13499004080721338486957494311618940989431
+ 13498904981611349475968483312708040099431
step 78: 26997909062332687962925977624326981088862
+ 26888018962342677952926978623326090979962
step 79: 53885928024675365915852956247653072068824
+ 42886027035674265925851956357642082958835
step 80: 96771955060349631841704912605295155027659
+ 95672055159250621940714813694306055917769
step 81: 192444010219600253782419726299601210945428
+ 824549012106992627914287352006912010444291
step 82: 1016993022326592881696707078306513221389719
+ 9179831223156038707076961882956232203996101
step 83: 10196824245482631588773668961262745425385820
+ 02858352454726216986637788513628454242869101
step 84: 13055176700208848575411457474891199668254921
+ 12945286699119847475411457584880200767155031
step 85: 26000463399328696050822915059771400435409952
+ 25990453400417795051922805069682399336400062
step 86: 51990916799746491102745720129453799771810014
+ 41001817799735492102754720119464799761909915
step 87: 92992734599481983205500440248918599533719929
+ 92991733599581984204400550238918499543729929
step 88: 185984468199063967409900990487837099077449858
+ 858944770990738784099009904769360991864489581
step 89: 1044929239189802751508910895257198090941939439
+ 9349391490908917525980198051572089819329294401
step 90: 10394320730098720277489108946829287910271233840
+ 04833217201978292864980198477202789003702349301
step 91: 15227537932077013142469307424032076913973583141
+ 14138537931967023042470396424131077023973572251
step 92: 29366075864044036184939703848163153937947155392
+ 29355174973935136184830793948163044046857066392
step 93: 58721250837979172369770497796326197984804221784
+ 48712240848979162369779407796327197973805212785
step 94: 107433491686958334739549905592653395958609434569
+ 965434906859593356295509945937433859686194334701
step 95: 1072868398546551691035059851530087255644803769270
+ 0729673084465527800351589505301961556458938682701
step 96: 1802541483012079491386649356832048812103742451971
+ 1791542473012188402386539466831949702103841452081
step 97: 3594083956024267893773188823663998514207583904052
+ 2504093857024158993663288813773987624206593804953
step 98: 6098177813048426887436477637437986138414177709005
+ 5009077714148316897347367746347886248403187718906
step 99: 11107255527196743784783845383785872386817365427911
+ 11972456371868327858738354838748734769172555270111
step 100: 23079711899065071643522200222534607155989920698022
+ 22089602998955170643522200222534617056099811797032
step 101: 45169314898020242287044400445069224212089732495054
+ 45059423798021242296054400444078224202089841396154
step 102: 90228738696041484583098800889147448414179573891208
+ 80219837597141484474198800889038548414069683782209
step 103: 170448576293182969057297601778185996828249257673417
+ 714376752942828699581877106792750969281392675844071
step 104: 884825329236011668639174708570936966109641933517488
+ 884715339146901669639075807471936866110632923528488
step 105: 1769540668382913338278250516042873832220274857045976
+ 6795407584720222383782406150528728333192838660459671
step 106: 8564948253103135722060656666571602165413113517505647
+ 7465057153113145612061756666560602275313013528494658
step 107: 16030005406216281334122413333132204440726127046000305
+ 50300064072162704440223133331422143318261260450003061
step 108: 66330069478378985774345546664554347758987387496003366
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5020089949 takes 108 iterations / steps to resolve into a 53 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] |
|---|
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 2,542,436 times since Saturday, March 9th, 2002.)
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