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                    REVERSAL-ADDITION PALINDROME TEST ON 13697

                    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 13697:
                    13697
                    + 79631
                    step 1: 93328
                    + 82339
                    step 2: 175667
                    + 766571
                    step 3: 942238
                    + 832249
                    step 4: 1774487
                    + 7844771
                    step 5: 9619258
                    + 8529169
                    step 6: 18148427
                    + 72484181
                    step 7: 90632608
                    + 80623609
                    step 8: 171256217
                    + 712652171
                    step 9: 883908388
                    + 883809388
                    step 10: 1767717776
                    + 6777177671
                    step 11: 8544895447
                    + 7445984458
                    step 12: 15990879905
                    + 50997809951
                    step 13: 66988689856
                    + 65898688966
                    step 14: 132887378822
                    + 228873788231
                    step 15: 361761167053
                    + 350761167163
                    step 16: 712522334216
                    + 612433225217
                    step 17: 1324955559433
                    + 3349555594231
                    step 18: 4674511153664
                    + 4663511154764
                    step 19: 9338022308428
                    + 8248032208339
                    step 20: 17586054516767
                    + 76761545068571
                    step 21: 94347599585338
                    + 83358599574349
                    step 22: 177706199159687
                    + 786951991607771
                    step 23: 964658190767458
                    + 854767091856469
                    step 24: 1819425282623927
                    + 7293262825249181
                    step 25: 9112688107873108
                    + 8013787018862119
                    step 26: 17126475126735227
                    + 72253762157462171
                    step 27: 89380237284197398
                    + 89379148273208398
                    step 28: 178759385557405796
                    + 697504755583957871
                    step 29: 876264141141363667
                    + 766363141141462678
                    step 30: 1642627282282826345
                    + 5436282822827262461
                    step 31: 7078910105110088806
                    + 6088800115010198707
                    step 32: 13167710220120287513
                    + 31578202102201776131
                    step 33: 44745912322322063644
                    + 44636022322321954744
                    step 34: 89381934644644018388
                    + 88381044644643918398
                    step 35: 177762979289287936786
                    + 687639782982979267771
                    step 36: 865402762272267204557
                    + 755402762272267204568
                    step 37: 1620805524544534409125
                    + 5219044354454255080261
                    step 38: 6839849878998789489386
                    13697 takes 38 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 2,095,801 times since Saturday, March 9th, 2002.)

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