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  • REVERSAL-ADDITION PALINDROME TEST ON 20889

    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 20889:
    20889
    + 98802
    step 1: 119691
    + 196911
    step 2: 316602
    + 206613
    step 3: 523215
    + 512325
    step 4: 1035540
    + 0455301
    step 5: 1490841
    + 1480941
    step 6: 2971782
    + 2871792
    step 7: 5843574
    + 4753485
    step 8: 10597059
    + 95079501
    step 9: 105676560
    + 065676501
    step 10: 171353061
    + 160353171
    step 11: 331706232
    + 232607133
    step 12: 564313365
    + 563313465
    step 13: 1127626830
    + 0386267211
    step 14: 1513894041
    + 1404983151
    step 15: 2918877192
    + 2917788192
    step 16: 5836665384
    + 4835666385
    step 17: 10672331769
    + 96713327601
    step 18: 107385659370
    + 073956583701
    step 19: 181342243071
    + 170342243181
    step 20: 351684486252
    + 252684486153
    step 21: 604368972405
    + 504279863406
    step 22: 1108648835811
    + 1185388468011
    step 23: 2294037303822
    + 2283037304922
    step 24: 4577074608744
    + 4478064707754
    step 25: 9055139316498
    + 8946139315509
    step 26: 18001278632007
    + 70023687210081
    step 27: 88024965842088
    + 88024856942088
    step 28: 176049822784176
    + 671487228940671
    step 29: 847537051724847
    + 748427150735748
    step 30: 1595964202460595
    + 5950642024695951
    step 31: 7546606227156546
    + 6456517226066457
    step 32: 14003123453223003
    + 30032235432130041
    step 33: 44035358885353044
    20889 takes 33 iterations / steps to resolve into a 17 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 2,061,678 times since Saturday, March 9th, 2002.)
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