|
REVERSAL-ADDITION
PALINDROME
TEST ON
10090899969901
|
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 10090899969901: |
10090899969901
+ 10996999809001
step 1: 21087899778902
+ 20987799878012
step 2: 42075699656914
+ 41965699657024
step 3: 84041399313938
+ 83931399314048
step 4: 167972798627986
+ 689726897279761
step 5: 857699695907747
+ 747709596996758
step 6: 1605409292904505
+ 5054092929045061
step 7: 6659502221949566
+ 6659491222059566
step 8: 13318993444009132
+ 23190044439981331
step 9: 36509037883990463
+ 36409938873090563
step 10: 72918976757081026
+ 62018075767981927
step 11: 134937052525062953
+ 359260525250739431
step 12: 494197577775802384
+ 483208577775791494
step 13: 977406155551593878
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step 14: 1855801311103198657
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step 15: 9424714322234284238
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step 16: 17749538644468458487
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step 17: 96235025089152053258
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step 18: 181470050287204106527
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step 19: 907071453069254180708
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step 20: 1714152906029608351417
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step 21: 8855690975235700865588
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step 22: 17711371050561491831176
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step 23: 84825190467066509142947
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step 24: 159749381033142918295795
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step 25: 757342200274473102243746
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step 26: 1404684401648945104487503
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step 27: 4462528417147406149351544
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step 30: 86108394420277202438391157
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step 31: 161227777840554404887771325
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step 32: 684405566245009453665493486
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step 35: 7233591938098019908282063217
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step 61: 90915119435546686255267575552402150908
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step 62: 171820239861104262510536240105893302817
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step 66: 16161238560483143504114042424740667321715
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step 67: 67873615165225567545254576563147250537876
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step 68: 135747120439362135090509153115403402175752
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step 71: 1452285397964604837982398748406459794483253
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step 72: 4976130377510653316915296132471157730305794
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step 73: 9951160755022395633840492266031315460622588
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step 74: 18803421400153702256780975631963521031234187
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step 75: 96946634412690615914689740852698621443665068
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step 76: 183003268825380241719488382804308242887330037
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step 77: 913037057068183650003373299946391771749630418
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step 78: 1727074004245377299995746600002773632500360737
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step 79: 9097704056609149300062222599930509056505068008
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step 80: 17106309113118199700014445199969928123009145917
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step 81: 89060499145301196699168886200769109254199506088
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step 82: 177121098290591393399437772400438219608398912186
+ 681219893806912834004277734993393195092890121771
step 83: 858340992097504227403715507393831414701289033957
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step 84: 1617671974204918365797421024698553820491588077815
+ 5187708851940283558964201247975638194024791767161
step 85: 6805380826145201924761622272674192014516379844976
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step 86: 13599870562299304839524344534348483039932660680062
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step 87: 39608477186292343323867888876942323439159168579593
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step 88: 79206063381485775648835777753774657768427346060286
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step 89: 147412127753972551296571555507659315526845682120583
+ 385021286548625513956705555175692155279357721214741
step 90: 532433414302598065253277110683351470806203403335324
+ 423533304302608074153386011772352560895203414334235
step 91: 955966718605206139406663122455704031701406817669559
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step 92: 1911933437209313269814217343822308963303913635339118
+ 8119335363193033698032283437124189623139027343391191
step 93: 10031268800402346967846500780946498586442940978730309
+ 90303787904924468589464908700564876964320400886213001
step 94: 100335056705326815557311409481511375550763341864943310
+ 013349468143367055573115184904113755518623507650533001
step 95: 113684524848693871130426594385625131069386849515476311
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step 96: 227359040797377831261953177881249162247783697940962622
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step 97: 453628090593765573523895366652608324386557494981916344
+ 443619189494755683423806256663598325375567395090826354
step 98: 897247280088521256947701623316206649762124890072742698
+ 896247270098421267946602613326107749652125880082742798
step 99: 1793494550186942524894304236642314399414250770155485496
+ 6945845510770524149934132466324034984252496810554943971
step 100: 8739340060957466674828436702966349383666747580710429467
+ 7649240170857476663839436692076348284766647590600439378
step 101: 16388580231814943338667873395042697668433395171310868845
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step 102: 71275381548974276825347497454380574351768336984519457206
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step 103: 131550873097937663540695005799860048704635584969037814423
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step 104: 455969604067423199948535074797360644750002324759415869554
+ 455968514957423200057446063797470535849991324760406969554
step 105: 911938119024846400005981138594831180599993649519822839108
+ 801938228915946399995081138495831189500004648420911839119
step 106: 1713876347940792800001062277090662370099998297940734678227
+ 7228764370497928999900732660907722601000082970497436783171
step 107: 8942640718438721799901794937998384971100081268438171461398
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step 108: 17874282436787343599913589776995779942200052546786341923896
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step 109: 87707196805551868600138587536963578474199586925549770171767
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step 110: 164424304600104837199286075073927157057300273741100639342545
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step 111: 709668240601252209203036826803297727740292012142107042767006
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step 112: 1310435481302493419495084554595606356370594914394213085633913
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step 113: 4503801284427427614445821090661560911176544058336244930974044
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step 115: 17816094258697621347794174462536353634814086342257078514015196
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step 123: 57776810881768307831553226775865256868762235513869297707910767775
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step 124: 115553512852547604663106453562730513726524471027739684426712635550
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step 125: 171089730477034542383280879190045550991879072394146429684927991061
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step 126: 331289459963959183876551857389101091083857154777391860458965971232
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step 127: 563469029818027377654003615769291193067615310455773819828920953365
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step 128: 1126828059646945755208017132529682386035131610912547540647841917730
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step 129: 1504019547107403207398178447836515255287448718938123037117350203941
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step 130: 2997040084224706425796356895662040411674897437875146084134809307992
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step 131: 5994079168539512841583704880423180814340883974850392158359609715984
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step 132: 10889258238078025772168498760857361627581768048701874317718229420979
+ 97902492281771347810784086718572616375806789486127752087083285298801
step 133: 108791750519849373582952585479429978003388557534829626404801514719780
+ 087917415108404626928435755883300879924974585259285373948915057197801
step 134: 196709165628254000511388341362730857928363142794115000353716571917581
+ 185719175617353000511497241363829758037263143883115000452826561907691
step 135: 382428341245607001022885582726560615965626286677230000806543133825272
+ 272528331345608000032776682626569516065627285588220100706542143824283
step 136: 654956672591215001055662265353130132031253572265450101513085277649555
+ 555946772580315101054562275352130231031353562266550100512195276659456
step 137: 1210903445171530102110224540705260363062607134532000202025280554309011
+ 1109034550825202020002354317062603630625070454220112010351715443090121
step 138: 2319937995996732122112578857767863993687677588752112212376995997399132
|
|
|
10090899969901 takes 138 iterations / steps to resolve into a 70 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 2,499,854 times since Saturday, March 9th, 2002.)
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