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                    REVERSAL-ADDITION PALINDROME TEST ON 15891

                    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 15891:
                    15891
                    + 19851
                    step 1: 35742
                    + 24753
                    step 2: 60495
                    + 59406
                    step 3: 119901
                    + 109911
                    step 4: 229812
                    + 218922
                    step 5: 448734
                    + 437844
                    step 6: 886578
                    + 875688
                    step 7: 1762266
                    + 6622671
                    step 8: 8384937
                    + 7394838
                    step 9: 15779775
                    + 57797751
                    step 10: 73577526
                    + 62577537
                    step 11: 136155063
                    + 360551631
                    step 12: 496706694
                    + 496607694
                    step 13: 993314388
                    + 883413399
                    step 14: 1876727787
                    + 7877276781
                    step 15: 9754004568
                    + 8654004579
                    step 16: 18408009147
                    + 74190080481
                    step 17: 92598089628
                    + 82698089529
                    step 18: 175296179157
                    + 751971692571
                    step 19: 927267871728
                    + 827178762729
                    step 20: 1754446634457
                    + 7544366444571
                    step 21: 9298813079028
                    + 8209703188929
                    step 22: 17508516267957
                    + 75976261580571
                    step 23: 93484777848528
                    + 82584877748439
                    step 24: 176069655596967
                    + 769695556960671
                    step 25: 945765212557638
                    + 836755212567549
                    step 26: 1782520425125187
                    + 7815215240252871
                    step 27: 9597735665378058
                    + 8508735665377959
                    step 28: 18106471330756017
                    + 71065703317460181
                    step 29: 89172174648216198
                    + 89161284647127198
                    step 30: 178333459295343396
                    + 693343592954333871
                    step 31: 871677052249677267
                    + 762776942250776178
                    step 32: 1634453994500453445
                    + 5443540054993544361
                    step 33: 7077994049493997806
                    + 6087993949404997707
                    step 34: 13165987998898995513
                    + 31559989889978956131
                    step 35: 44725977888877951644
                    + 44615977888877952744
                    step 36: 89341955777755904388
                    + 88340955777755914398
                    step 37: 177682911555511818786
                    + 687818115555119286771
                    step 38: 865501027110631105557
                    + 755501136011720105568
                    step 39: 1621002163122351211125
                    + 5211121532213612001261
                    step 40: 6832123695335963212386
                    15891 takes 40 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 2,095,808 times since Saturday, March 9th, 2002.)

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