山水娱乐

  • REVERSAL-ADDITION PALINDROME TEST ON 1005744

    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 1005744:
    1005744
    + 4475001
    step 1: 5480745
    + 5470845
    step 2: 10951590
    + 09515901
    step 3: 20467491
    + 19476402
    step 4: 39943893
    + 39834993
    step 5: 79778886
    + 68887797
    step 6: 148666683
    + 386666841
    step 7: 535333524
    + 425333535
    step 8: 960667059
    + 950766069
    step 9: 1911433128
    + 8213341191
    step 10: 10124774319
    + 91347742101
    step 11: 101472516420
    + 024615274101
    step 12: 126087790521
    + 125097780621
    step 13: 251185571142
    + 241175581152
    step 14: 492361152294
    + 492251163294
    step 15: 984612315588
    + 885513216489
    step 16: 1870125532077
    + 7702355210781
    step 17: 9572480742858
    + 8582470842759
    step 18: 18154951585617
    + 71658515945181
    step 19: 89813467530798
    + 89703576431898
    step 20: 179517043962696
    + 696269340715971
    step 21: 875786384678667
    + 766876483687578
    step 22: 1642662868366245
    + 5426638682662461
    step 23: 7069301551028706
    + 6078201551039607
    step 24: 13147503102068313
    + 31386020130574131
    step 25: 44533523232642444
    + 44424623232533544
    step 26: 88958146465175988
    + 88957156464185988
    step 27: 177915302929361976
    + 679163929203519771
    step 28: 857079232132881747
    + 747188231232970758
    step 29: 1604267463365852505
    + 5052585633647624061
    step 30: 6656853097013476566
    + 6656743107903586566
    step 31: 13313596204917063132
    + 23136071940269531331
    step 32: 36449668145186594463
    + 36449568154186694463
    step 33: 72899236299373288926
    + 62988237399263299827
    step 34: 135887473698636588753
    + 357885636896374788531
    step 35: 493773110595011377284
    + 482773110595011377394
    step 36: 976546221190022754678
    + 876457220091122645679
    step 37: 1853003441281145400357
    + 7530045411821443003581
    step 38: 9383048853102588403938
    + 8393048852013588403839
    step 39: 17776097705116176807777
    + 77770867161150779067771
    step 40: 95546964866266955875548
    + 84557855966266846964559
    step 41: 180104820832533802840107
    + 701048208335238028401081
    step 42: 881153029167771831241188
    + 881142138177761920351188
    step 43: 1762295167345533751592376
    + 6732951573355437615922671
    step 44: 8495246740700971367515047
    + 7405157631790070476425948
    step 45: 15900404372491041843940995
    + 59904934814019427340400951
    step 46: 75805339186510469184341946
    + 64914348196401568193350857
    step 47: 140719687382912037377692803
    + 308296773730219283786917041
    step 48: 449016461113131321164609844
    + 448906461123131311164610944
    step 49: 897922922236262632329220788
    + 887022923236262632229229798
    step 50: 1784945845472525264558450586
    + 6850548554625252745485494871
    step 51: 8635494400097778010043945457
    + 7545493400108777900044945368
    step 52: 16180987800206555910088890825
    + 52809888001955560200878908161
    step 53: 68990875802162116110967798986
    + 68989776901161126120857809986
    step 54: 137980652703323242231825608972
    + 279806528132242323307256089731
    step 55: 417787180835565565539081698703
    + 307896180935565565538081787714
    step 56: 725683361771131131077163486417
    + 714684361770131131177163386527
    step 57: 1440367723541262262254326872944
    + 4492786234522622621453277630441
    step 58: 5933153958063884883707604503385
    + 5833054067073884883608593513395
    step 59: 11766208025137769767316198016780
    + 08761089161376796773152080266711
    step 60: 20527297186514566540468278283491
    + 19438287286404566541568179272502
    step 61: 39965584472919133082036457555993
    + 39955575463028033191927448556993
    step 62: 79921159935947166273963906112986
    + 68921160936937266174953995112997
    step 63: 148842320872884432448917901225983
    + 389522109719844234488278023248841
    step 64: 538364430592728666937195924474824
    + 428474429591739666827295034463835
    step 65: 966838860184468333764490958938659
    + 956839859094467333864481068838669
    step 66: 1923678719278935667628972027777328
    + 8237777202798267665398729178763291
    step 67: 10161455922077203333027701206540619
    + 91604560210772033330277022955416101
    step 68: 101766016132849236663304724161956720
    + 027659161427403366632948231610667101
    step 69: 129425177560252603296252955772623821
    + 128326277559252692306252065771524921
    step 70: 257751455119505295602505021544148742
    + 247841445120505206592505911554157752
    step 71: 505592900240010502195010933098306494
    + 494603890339010591205010042009295505
    step 72: 1000196790579021093400020975107601999
    + 9991067015790200043901209750976910001
    step 73: 10991263806369221137301230726084512000
    + 00021548062703210373112296360836219901
    step 74: 11012811869072431510413527086920731901
    + 10913702968072531401513427096811821011
    step 75: 21926514837144962911926954183732552912
    + 21925523738145962911926944173841562912
    step 76: 43852038575290925823853898357574115824
    + 42851147575389835832852909257583025834
    step 77: 86703186150680761656706807615157141658
    + 85614175151670860765616708605168130768
    step 78: 172317361302351622422323516220325272426
    + 624272523022615323224226153203163713271
    step 79: 796589884324966945646549669423488985697
    1005744 takes 79 iterations / steps to resolve into a 39 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.)

    DigitsNumberResult
    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 2,061,639 times since Saturday, March 9th, 2002.)
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