REVERSAL-ADDITION
PALINDROME
TEST ON
60000180709
|
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 60000180709: |
60000180709
+ 90708100006
step 1: 150708280715
+ 517082807051
step 2: 667791087766
+ 667780197766
step 3: 1335571285532
+ 2355821755331
step 4: 3691393040863
+ 3680403931963
step 5: 7371796972826
+ 6282796971737
step 6: 13654593944563
+ 36544939545631
step 7: 50199533490194
+ 49109433599105
step 8: 99308967089299
+ 99298076980399
step 9: 198607044069698
+ 896960440706891
step 10: 1095567484776589
+ 9856774847655901
step 11: 10952342332432490
+ 09423423324325901
step 12: 20375765656758391
+ 19385765656757302
step 13: 39761531313515693
+ 39651531313516793
step 14: 79413062627032486
+ 68423072626031497
step 15: 147836135253063983
+ 389360352531638741
step 16: 537196487784702724
+ 427207487784691735
step 17: 964403975569394459
+ 954493965579304469
step 18: 1918897941148698928
+ 8298968411497988191
step 19: 10217866352646687119
+ 91178664625366871201
step 20: 101396530978013558320
+ 023855310879035693101
step 21: 125251841857049251421
+ 124152940758148152521
step 22: 249404782615197403942
+ 249304791516287404942
step 23: 498709574131484808884
+ 488808484131475907894
step 24: 987518058262960716778
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step 25: 1865135127525811532567
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step 26: 9517486312783026848248
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step 27: 17945972516655163695407
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step 28: 88405608672316691650378
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step 29: 175711228333644372300866
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step 31: 1578528993659955299835785
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step 32: 7453918919259519298094536
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step 33: 13808827848419048496288083
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step 34: 51897097332510533369168914
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step 35: 93883293666012056748248729
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step 36: 186667578431033123387487568
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step 37: 1052452361752363258263254249
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step 46: 1047597098573607696366890705650
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step 49: 5241574121941408931492214661325
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step 50: 10473238244882806972983429412750
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step 53: 52699713823252189116331741699625
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step 54: 105399328536613387241564573499250
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step 55: 158393704001756170558200397492751
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step 56: 315688497004611242215300804886602
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step 58: 1033754900115256968653502109446340
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step 59: 1470203912168825665178612204019641
+ 1469104022168715665288612193020741
step 60: 2939307934337541330467224397040382
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step 61: 5769715868565181661924558794079774
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step 62: 10549420847119473323740217479259449
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step 63: 105044718318324205661231392281753950
+ 059357182293132166502423813817440501
step 64: 164401900611456372163655206099194451
+ 154491990602556361273654116009104461
step 65: 318893891214012733437309322108298912
+ 219892801223903734337210412198398813
step 66: 538786692437916467774519734306697725
+ 527796603437915477764619734296687835
step 67: 1066583295875831945539139468603385560
+ 0655833068649319355491385785923856601
step 68: 1722416364525151301030525254527242161
+ 1612427254525250301031515254636142271
step 69: 3334843619050401602062040509163384432
+ 2344833619050402602061040509163484333
step 70: 5679677238100804204123081018326868765
+ 5678686238101803214024080018327769765
step 71: 11358363476202607418147161036654638530
+ 03583645663016174181470620267436385311
step 72: 14942009139218781599617781304091023841
+ 14832019040318771699518781293190024941
step 73: 29774028179537553299136562597281048782
+ 28784018279526563199235573597182047792
step 74: 58558046459064116498372136194463096574
+ 47569036449163127389461146095464085585
step 75: 106127082908227243887833282289927182159
+ 951281729982282338788342722809280721601
step 76: 1057408812890509582676176005099207903760
+ 0673097029905006716762859050982188047501
step 77: 1730505842795516299439035056081395951261
+ 1621595931806505309349926155972485050371
step 78: 3352101774602021608788961212053881001632
+ 2361001883502121698878061202064771012533
step 79: 5713103658104143307667022414118652014165
+ 5614102568114142207667033414018563013175
step 80: 11327206226218285515334055828137215027340
+ 04372051273182855043351558281262260272311
step 81: 15699257499401140558685614109399475299651
+ 15699257499390141658685504110499475299651
step 82: 31398514998791282217371118219898950599302
+ 20399505989891281117371228219789941589313
step 83: 51798020988682563334742346439688892188615
+ 51688129888693464324743336528688902089715
step 84: 103486150877376027659485682968377794278330
+ 033872497773869286584956720673778051684301
step 85: 137358648651245314244442403642155845962631
+ 136269548551246304244442413542156846853731
step 86: 273628197202491618488884817184312692816362
+ 263618296213481718488884816194202791826372
step 87: 537246493415973336977769633378515484642734
+ 437246484515873336967779633379514394642735
step 88: 974492977931846673945549266758029879285469
+ 964582978920857662945549376648139779294479
step 89: 1939075956852704336891098643406169658579948
+ 8499758569616043468901986334072586595709391
step 90: 10438834526468747805793084977478756254289339
+ 93398245265787477948039750874786462543883401
step 91: 103837079792256225753832835852265218798172740
+ 047271897812562258538238357522652297970738301
step 92: 151108977604818484292071193374917516768911041
+ 140119867615719473391170292484818406779801151
step 93: 291228845220537957683241485859735923548712192
+ 291217845329537958584142386759735022548822192
step 94: 582446690550075916267383872619470946097534384
+ 483435790649074916278383762619570055096644285
step 95: 1065882481199150832545767635239041001194178669
+ 9668714911001409325367675452380519911842885601
step 96: 10734597392200560157913443087619560913037064270
+ 07246073031906591678034431975106500229379543701
step 97: 17980670424107151835947875062726061142416607971
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step 98: 35951331848223214562005750016541231284824216942
+ 24961242848213214561005750026541232284813315953
step 99: 60912574696436429123011500043082463569637532895
+ 59823573696536428034000511032192463469647521906
step 100: 120736148392972857157012011075274927039285054801
+ 108450582930729472570110210751758279293841637021
step 101: 229186731323702329727122221827033206333126691822
+ 228196621333602330728122221727923207323137681922
step 102: 457383352657304660455244443554956413656264373744
+ 447373462656314659455344442554066403756253383754
step 103: 904756815313619319910588886109022817412517757498
+ 894757715214718220901688885019913916313518657409
step 104: 1799514530528337540812277771128936733726036414907
+ 7094146306273376398211777722180457338250354159971
step 105: 8893660836801713939024055493309394071976390574878
+ 8784750936791704939033945504209393171086380663988
step 106: 17678411773593418878058000997518787243062771238866
+ 66883217726034278781579900085087881439537711487671
step 107: 84561629499627697659637901082606668682600482726537
+ 73562728400628686660628010973695679672699492616548
step 108: 158124357900256384320265912056302348355299975343085
+ 580343579992553843203650219562023483652009753421851
step 109: 738467937892810227523916131618325832007309728764936
+ 639467827903700238523816131619325722018298739764837
step 110: 1377935765796510466047732263237651554025608468529773
+ 3779258648065204551567323622377406640156975675397731
step 111: 5157194413861715017615055885615058194182584143927504
+ 4057293414852814918505165885505167105171683144917515
step 112: 9214487828714529936120221771120225299354267288845019
+ 9105488827624539925220211771220216399254178287844129
step 113: 18319976656339069861340433542340441698608445576689148
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step 114: 102518644210819759475744758075744758594701811244680529
+ 925086442118107495857447570857447574957918012446815201
step 115: 1027605086328927255333192328933192333552619823691495730
+ 0375941963289162553332913398232913335527298236805067201
step 116: 1403547049618089808666105727166105669079918060496562931
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step 117: 2796203990226289518331122344441122337169726229904015972
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step 118: 5591308089452569135663333788873333675329552450897042944
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step 119: 10083716069995128371426667577746667340649205000705074899
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step 120: 109930766770045422975803332355323329758031364996766812900
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step 121: 119149434469508553833726655908556638337255905074433852801
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step 122: 227407768940018106567563311718113265675611711038868794712
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step 123: 444905637770135223144125623535226631441213521088736499434
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step 124: 879900275650260535288262246070553152882536052166473008878
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step 125: 1758700650311511170576513601141195415765071114223045018856
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step 126: 8346806053535622876251659512552258572515782265353605097427
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step 127: 15594711117071245751404418035104418134042564530707111183865
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step 128: 72432822287774792275447599475257499574458318747778222933416
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step 129: 133866744575549573660895198950514999148915548495556445756843
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step 130: 482524289231144419180737198365574890746981924441131893425174
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step 131: 954048687362288848370384296841138782484063838882264875850458
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step 132: 1808107265824577686730868584672287474967137687764528662690917
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step 133: 8999069934079255554048563332495052333647514555518814289708998
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step 134: 17997149758267411108206026665000994667305919111048518689318996
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step 135: 87978548439851422300156403314901051329366199222524804483498967
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step 136: 164967986880693944599322795629911992659831299544940697968086945
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step 137: 714648856676743390591461751929031919257055294994336786657856406
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step 138: 1319307613364376890084012504848162848414219490087684463316702823
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step 139: 4601383747009244691033136653330781332466324291074419096483741954
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step 140: 9192857593918389392957373295662651666032637593038848103957573018
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step 141: 17296615186936877696914735602324214331956375185978686297915155937
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step 142: 91251767166205565655072101515665456652610117155656550266066825208
+ 80252866066205565655171101625665456651510127055656550266176715219
step 143: 171504633232411131310243203141330913304120244211313100532243540427
+ 724045342235001313112442021403319033141302342013131114232336405171
step 144: 895549975467412444422685224544649946445422586224444214764579945598
|
|
60000180709 takes 144 iterations / steps to resolve into a 66 digit palindrome.
|
REVERSAL-ADDITION
PALINDROME
RECORDS
|
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!
|
[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 2,531,643 times since Saturday, March 9th, 2002.)
|