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REVERSAL-ADDITION
PALINDROME
TEST ON
140669390
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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 140669390: |
140669390
+ 093966041
step 1: 234635431
+ 134536432
step 2: 369171863
+ 368171963
step 3: 737343826
+ 628343737
step 4: 1365687563
+ 3657865631
step 5: 5023553194
+ 4913553205
step 6: 9937106399
+ 9936017399
step 7: 19873123798
+ 89732137891
step 8: 109605261689
+ 986162506901
step 9: 1095767768590
+ 0958677675901
step 10: 2054445444491
+ 1944445444502
step 11: 3998890888993
+ 3998880988993
step 12: 7997771877986
+ 6897781777997
step 13: 14895553655983
+ 38955635559841
step 14: 53851189215824
+ 42851298115835
step 15: 96702487331659
+ 95613378420769
step 16: 192315865752428
+ 824257568513291
step 17: 1016573434265719
+ 9175624343756101
step 18: 10192197778021820
+ 02812087779129101
step 19: 13004285557150921
+ 12905175558240031
step 20: 25909461115390952
+ 25909351116490952
step 21: 51818812231881904
+ 40918813221881815
step 22: 92737625453763719
+ 91736735452673729
step 23: 184474360906437448
+ 844734609063474481
step 24: 1029208969969911929
+ 9291199699698029201
step 25: 10320408669667941130
+ 03114976696680402301
step 26: 13435385366348343431
+ 13434384366358353431
step 27: 26869769732706696862
+ 26869660723796796862
step 28: 53739430456503493724
+ 42739430565403493735
step 29: 96478861021906987459
+ 95478960912016887469
step 30: 191957821933923874928
+ 829478329339128759191
step 31: 1021436151273052634119
+ 9114362503721516341201
step 32: 10135798654994568975320
+ 02357986549945689753101
step 33: 12493785204940258728421
+ 12482785204940258739421
step 34: 24976570409880517467842
+ 24876471508890407567942
step 35: 49853041918770925035784
+ 48753052907781914035894
step 36: 98606094826552839071678
+ 87617093825562849060689
step 37: 186223188652115688132367
+ 763231886511256881322681
step 38: 949455075163372569455048
+ 840554965273361570554949
step 39: 1790010040436734140009997
+ 7999000414376340400100971
step 40: 9789010454813074540110968
+ 8690110454703184540109879
step 41: 18479120909516259080220847
+ 74802208095261590902197481
step 42: 93281329004777849982418328
+ 82381428994877740092318239
step 43: 175662757999655590074736567
+ 765637470095556999757266571
step 44: 941300228095212589832003138
+ 831300238985212590822003149
step 45: 1772600467080425180654006287
+ 7826004560815240807640062771
step 46: 9598605027895665988294069058
+ 8509604928895665987205068959
step 47: 18108209956791331975499138017
+ 71083199457913319765990280181
step 48: 89191409414704651741489418198
+ 89181498414715640741490419198
step 49: 178372907829420292482979837396
+ 693738979284292024928709273871
step 50: 872111887113712317411689111267
+ 762111986114713217311788111278
step 51: 1634223873228425534723477222545
+ 5452227743274355248223783224361
step 52: 7086451616502780782947260446906
+ 6096440627492870872056161546807
step 53: 13182892243995651655003421993713
+ 31739912430055615659934229828131
step 54: 44922804674051267314937651821844
+ 44812815673941376215047640822944
step 55: 89735620347992643529985292644788
+ 88744629258992534629974302653798
step 56: 178480249606985178159959595298586
+ 685892595959951871589606942084871
step 57: 864372845566937049749566537383457
+ 754383735665947940739665548273468
step 58: 1618756581232884990489232085656925
+ 5296565802329840994882321856578161
step 59: 6915322383562725985371553942235086
+ 6805322493551735895272653832235196
step 60: 13720644877114461880644207774470282
+ 28207447770244608816441177844602731
step 61: 41928092647359070697085385619073013
+ 31037091658358079607095374629082914
step 62: 72965184305717150304180760248155927
+ 72955184206708140305171750348156927
step 63: 145920368512425290609352510596312854
+ 458213695015253906092524215863029541
step 64: 604134063527679196701876726459342395
+ 593243954627678107691976725360431406
step 65: 1197378018155357304393853451819773801
+ 1083779181543583934037535518108737911
step 66: 2281157199698941238431388969928511712
+ 2171158299698831348321498969917511822
step 67: 4452315499397772586752887939846023534
+ 4353206489397882576852777939945132544
step 68: 8805521988795655163605665879791156078
+ 8706511979785665063615565978891255088
step 69: 17512033968581320227221231858682411166
+ 66111428685813212272202318586933021571
step 70: 83623462654394532499423550445615432737
+ 73723451654405532499423549345626432638
step 71: 157346914308800064998847099791241865375
+ 573568142197990748899460008803419643751
step 72: 730915056506790813898307108594661509126
+ 621905166495801703898318097605650519037
step 73: 1352820223002592517796625206200312028163
+ 3618202130026025266977152952003220282531
step 74: 4971022353028617784773778158203532310694
+ 4960132353028518773774877168203532201794
step 75: 9931154706057136558548655326407064512488
+ 8842154607046235568458556317506074511399
step 76: 18773309313103372127007211643913139023887
+ 78832093131934611270072127330131390337781
step 77: 97605402445037983397079338974044529361668
+ 86616392544047983397079338973054420450679
step 78: 184221794989085966794158677947098949812347
+ 743218949890749776851497669580989497122481
step 79: 927440744879835743645656347528088446934828
+ 828439644880825743656546347538978447044729
step 80: 1755880389760661487302202695067066893979557
+ 7559793986607605962022037841660679830885571
step 81: 9315674376368267449324240536727746724865128
+ 8215684276477276350424239447628636734765139
step 82: 17531358652845543799748479984356383459630267
+ 76203695438365348997484799734554825685313571
step 83: 93735054091210892797233279718911209144943838
+ 83834944190211981797233279729801219045053739
step 84: 177569998281422874594466559448712428189997577
+ 775799981824217844955664495478224182899965771
step 85: 953369980105640719550131054926936611089963348
+ 843369980116639629450131055917046501089963359
step 86: 1796739960222280349000262110843983112179926707
+ 7076299712113893480112620009430822220699376971
step 87: 8873039672336173829112882120274805332879303678
+ 8763039782335084720212882119283716332769303788
step 88: 17636079454671258549325764239558521665648607466
+ 66470684656612585593246752394585217645497063671
step 89: 84106764111283844142572516634143739311145671137
+ 73117654111393734143661527524144838211146760148
step 90: 157224418222677578286234044158288577522292431285
+ 582134292225775882851440432682875776222814422751
step 91: 739358710448453461137674476841164353745106854036
+ 630458601547353461148674476731164354844017853937
step 92: 1369817311995806922286348953572328708589124707973
+ 3797074219858078232753598436822296085991137189631
step 93: 5166891531853885155039947390394624794580261897604
+ 4067981620854974264930937499305515883581351986615
step 94: 9234873152708859419970884889700140678161613884219
+ 9124883161618760410079884880799149588072513784329
step 95: 18359756314327619830050769770499290266234127668548
+ 84586672143266209299407796705003891672341365795381
step 96: 102946428457593829129458566475503181938575493463929
+ 929364394575839181305574665854921928395754824649201
step 97: 1032310823033433010435033232330425110334330318113130
+ 0313118130334330115240332323305340103343303280132301
step 98: 1345428953367763125675365555635765213677633598245431
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140669390 takes 98 iterations / steps to resolve into a 52 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
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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 2,549,744 times since Saturday, March 9th, 2002.)
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