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                    REVERSAL-ADDITION PALINDROME TEST ON 1008628

                    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 1008628:
                    1008628
                    + 8268001
                    step 1: 9276629
                    + 9266729
                    step 2: 18543358
                    + 85334581
                    step 3: 103877939
                    + 939778301
                    step 4: 1043656240
                    + 0426563401
                    step 5: 1470219641
                    + 1469120741
                    step 6: 2939340382
                    + 2830439392
                    step 7: 5769779774
                    + 4779779675
                    step 8: 10549559449
                    + 94495594501
                    step 9: 105045153950
                    + 059351540501
                    step 10: 164396694451
                    + 154496693461
                    step 11: 318893387912
                    + 219783398813
                    step 12: 538676786725
                    + 527687676835
                    step 13: 1066364463560
                    + 0653644636601
                    step 14: 1720009100161
                    + 1610019000271
                    step 15: 3330028100432
                    + 2340018200333
                    step 16: 5670046300765
                    + 5670036400765
                    step 17: 11340082701530
                    + 03510728004311
                    step 18: 14850810705841
                    + 14850701805841
                    step 19: 29701512511682
                    + 28611521510792
                    step 20: 58313034022474
                    + 47422043031385
                    step 21: 105735077053859
                    + 958350770537501
                    step 22: 1064085847591360
                    + 0631957485804601
                    step 23: 1696043333395961
                    + 1695933333406961
                    step 24: 3391976666802922
                    + 2292086666791933
                    step 25: 5684063333594855
                    + 5584953333604865
                    step 26: 11269016667199720
                    + 02799176661096211
                    step 27: 14068193328295931
                    + 13959282339186041
                    step 28: 28027475667481972
                    + 27918476657472082
                    step 29: 55945952324954054
                    + 45045942325954955
                    step 30: 100991894650909009
                    + 900909056498199001
                    step 31: 1001900951149108010
                    + 0108019411590091001
                    step 32: 1109920362739199011
                    + 1109919372630299011
                    step 33: 2219839735369498022
                    + 2208949635379389122
                    step 34: 4428789370748887144
                    + 4417888470739878244
                    step 35: 8846677841488765388
                    + 8835678841487766488
                    step 36: 17682356682976531876
                    + 67813567928665328671
                    step 37: 85495924611641860547
                    + 74506814611642959458
                    step 38: 160002739223284820005
                    + 500028482322937200061
                    step 39: 660031221546222020066
                    + 660020222645122130066
                    step 40: 1320051444191344150132
                    + 2310514431914441500231
                    step 41: 3630565876105785650363
                    + 3630565875016785650363
                    step 42: 7261131751122571300726
                    + 6270031752211571311627
                    step 43: 13531163503334142612353
                    + 35321624143330536113531
                    step 44: 48852787646664678725884
                    1008628 takes 44 iterations / steps to resolve into a 23 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 2,095,878 times since Saturday, March 9th, 2002.)

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