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  • REVERSAL-ADDITION PALINDROME TEST ON 10853

    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 10853:
    10853
    + 35801
    step 1: 46654
    + 45664
    step 2: 92318
    + 81329
    step 3: 173647
    + 746371
    step 4: 920018
    + 810029
    step 5: 1730047
    + 7400371
    step 6: 9130418
    + 8140319
    step 7: 17270737
    + 73707271
    step 8: 90978008
    + 80087909
    step 9: 171065917
    + 719560171
    step 10: 890626088
    + 880626098
    step 11: 1771252186
    + 6812521771
    step 12: 8583773957
    + 7593773858
    step 13: 16177547815
    + 51874577161
    step 14: 68052124976
    + 67942125086
    step 15: 135994250062
    + 260052499531
    step 16: 396046749593
    + 395947640693
    step 17: 791994390286
    + 682093499197
    step 18: 1474087889483
    + 3849887804741
    step 19: 5323975694224
    + 4224965793235
    step 20: 9548941487459
    + 9547841498459
    step 21: 19096782985918
    + 81958928769091
    step 22: 101055711755009
    + 900557117550101
    step 23: 1001612829305110
    + 0115039282161001
    step 24: 1116652111466111
    + 1116641112566111
    step 25: 2233293224032222
    + 2222304223923322
    step 26: 4455597447955544
    10853 takes 26 iterations / steps to resolve into a 16 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 2,061,654 times since Saturday, March 9th, 2002.)
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