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  • REVERSAL-ADDITION PALINDROME TEST ON 80359

    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 80359:
    80359
    + 95308
    step 1: 175667
    + 766571
    step 2: 942238
    + 832249
    step 3: 1774487
    + 7844771
    step 4: 9619258
    + 8529169
    step 5: 18148427
    + 72484181
    step 6: 90632608
    + 80623609
    step 7: 171256217
    + 712652171
    step 8: 883908388
    + 883809388
    step 9: 1767717776
    + 6777177671
    step 10: 8544895447
    + 7445984458
    step 11: 15990879905
    + 50997809951
    step 12: 66988689856
    + 65898688966
    step 13: 132887378822
    + 228873788231
    step 14: 361761167053
    + 350761167163
    step 15: 712522334216
    + 612433225217
    step 16: 1324955559433
    + 3349555594231
    step 17: 4674511153664
    + 4663511154764
    step 18: 9338022308428
    + 8248032208339
    step 19: 17586054516767
    + 76761545068571
    step 20: 94347599585338
    + 83358599574349
    step 21: 177706199159687
    + 786951991607771
    step 22: 964658190767458
    + 854767091856469
    step 23: 1819425282623927
    + 7293262825249181
    step 24: 9112688107873108
    + 8013787018862119
    step 25: 17126475126735227
    + 72253762157462171
    step 26: 89380237284197398
    + 89379148273208398
    step 27: 178759385557405796
    + 697504755583957871
    step 28: 876264141141363667
    + 766363141141462678
    step 29: 1642627282282826345
    + 5436282822827262461
    step 30: 7078910105110088806
    + 6088800115010198707
    step 31: 13167710220120287513
    + 31578202102201776131
    step 32: 44745912322322063644
    + 44636022322321954744
    step 33: 89381934644644018388
    + 88381044644643918398
    step 34: 177762979289287936786
    + 687639782982979267771
    step 35: 865402762272267204557
    + 755402762272267204568
    step 36: 1620805524544534409125
    + 5219044354454255080261
    step 37: 6839849878998789489386
    80359 takes 37 iterations / steps to resolve into a 22 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 2,061,681 times since Saturday, March 9th, 2002.)
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