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                    REVERSAL-ADDITION PALINDROME TEST ON 89

                    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 89:
                    89
                    + 98
                    step 1: 187
                    + 781
                    step 2: 968
                    + 869
                    step 3: 1837
                    + 7381
                    step 4: 9218
                    + 8129
                    step 5: 17347
                    + 74371
                    step 6: 91718
                    + 81719
                    step 7: 173437
                    + 734371
                    step 8: 907808
                    + 808709
                    step 9: 1716517
                    + 7156171
                    step 10: 8872688
                    + 8862788
                    step 11: 17735476
                    + 67453771
                    step 12: 85189247
                    + 74298158
                    step 13: 159487405
                    + 504784951
                    step 14: 664272356
                    + 653272466
                    step 15: 1317544822
                    + 2284457131
                    step 16: 3602001953
                    + 3591002063
                    step 17: 7193004016
                    + 6104003917
                    step 18: 13297007933
                    + 33970079231
                    step 19: 47267087164
                    + 46178076274
                    step 20: 93445163438
                    + 83436154439
                    step 21: 176881317877
                    + 778713188671
                    step 22: 955594506548
                    + 845605495559
                    step 23: 1801200002107
                    + 7012000021081
                    step 24: 8813200023188
                    89 takes 24 iterations / steps to resolve into a 13 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 2,095,704 times since Saturday, March 9th, 2002.)

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