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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 2,095,795 times since Saturday, March 9th, 2002.)

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