山水娱乐

  • REVERSAL-ADDITION PALINDROME TEST ON 150296

    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 150296:
    150296
    + 692051
    step 1: 842347
    + 743248
    step 2: 1585595
    + 5955851
    step 3: 7541446
    + 6441457
    step 4: 13982903
    + 30928931
    step 5: 44911834
    + 43811944
    step 6: 88723778
    + 87732788
    step 7: 176456566
    + 665654671
    step 8: 842111237
    + 732111248
    step 9: 1574222485
    + 5842224751
    step 10: 7416447236
    + 6327446147
    step 11: 13743893383
    + 38339834731
    step 12: 52083728114
    + 41182738025
    step 13: 93266466139
    + 93166466239
    step 14: 186432932378
    + 873239234681
    step 15: 1059672167059
    + 9507612769501
    step 16: 10567284936560
    + 06563948276501
    step 17: 17131233213061
    + 16031233213171
    step 18: 33162466426232
    + 23262466426133
    step 19: 56424932852365
    + 56325823942465
    step 20: 112750756794830
    + 038497657057211
    step 21: 151248413852041
    + 140258314842151
    step 22: 291506728694192
    + 291496827605192
    step 23: 583003556299384
    + 483992655300385
    step 24: 1066996211599769
    + 9679951126996601
    step 25: 10746947338596370
    + 07369583374964701
    step 26: 18116530713561071
    + 17016531703561181
    step 27: 35133062417122252
    + 25222171426033153
    step 28: 60355233843155405
    + 50455134833255306
    step 29: 110810368676410711
    + 117014676863018011
    step 30: 227825045539428722
    + 227824935540528722
    step 31: 455649981079957444
    + 444759970189946554
    step 32: 900409951269903998
    + 899309962159904009
    step 33: 1799719913429808007
    + 7008089243199179971
    step 34: 8807809156628987978
    + 8797898266519087088
    step 35: 17605707423148075066
    + 66057084132470750671
    step 36: 83662791555618825737
    + 73752881655519726638
    step 37: 157415673211138552375
    + 573255831112376514751
    step 38: 730671504323515067126
    + 621760515323405176037
    step 39: 1352432019646920243163
    + 3613420296469102342531
    step 40: 4965852316116022585694
    + 4965852206116132585694
    step 41: 9931704522232155171388
    + 8831715512322254071399
    step 42: 18763420034554409242787
    + 78724290445543002436781
    step 43: 97487710480097411679568
    + 86597611479008401778479
    step 44: 184085321959105813458047
    + 740854318501959123580481
    step 45: 924939640461064937038528
    + 825830739460164046939429
    step 46: 1750770379921228983977957
    + 7597793898221299730770571
    step 47: 9348564278142528714748528
    + 8258474178252418724658439
    step 48: 17607038456394947439406967
    + 76960493474949365483070671
    step 49: 94567531931344312922477638
    + 83677422921344313913576549
    step 50: 178244954852688626836054187
    + 781450638626886258459442871
    step 51: 959695593479574885295497058
    + 850794592588475974395596959
    step 52: 1810490186068050859691094017
    + 7104901969580508606810940181
    step 53: 8915392155648559466502034198
    + 8914302056649558465512935198
    step 54: 17829694212298117932014969396
    + 69396941023971189221249692871
    step 55: 87226635236269307153264662267
    + 76226646235170396263253662278
    step 56: 163453281471439703416518324545
    + 545423815614307934174182354361
    step 57: 708877097085747637590700678906
    + 609876007095736747580790778807
    step 58: 1318753104181484385171491457713
    + 3177541941715834841814013578131
    step 59: 4496295045897319226985505035844
    + 4485305055896229137985405926944
    step 60: 8981600101793548364970910962788
    + 8872690190794638453971010061898
    step 61: 17854290292588186818941921024686
    + 68642012914981868188529209245871
    step 62: 86496303207570055007471130270557
    + 75507203117470055007570230369468
    step 63: 162003506325040110015041360640025
    + 520046063140510011040523605300261
    step 64: 682049569465550121055564965940286
    150296 takes 64 iterations / steps to resolve into a 33 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 2,061,625 times since Saturday, March 9th, 2002.)
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