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                    REVERSAL-ADDITION PALINDROME TEST ON 1001699

                    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 1001699:
                    1001699
                    + 9961001
                    step 1: 10962700
                    + 00726901
                    step 2: 11689601
                    + 10698611
                    step 3: 22388212
                    + 21288322
                    step 4: 43676534
                    + 43567634
                    step 5: 87244168
                    + 86144278
                    step 6: 173388446
                    + 644883371
                    step 7: 818271817
                    + 718172818
                    step 8: 1536444635
                    + 5364446351
                    step 9: 6900890986
                    + 6890980096
                    step 10: 13791871082
                    + 28017819731
                    step 11: 41809690813
                    + 31809690814
                    step 12: 73619381627
                    + 72618391637
                    step 13: 146237773264
                    + 462377732641
                    step 14: 608615505905
                    + 509505516806
                    step 15: 1118121022711
                    + 1172201218111
                    step 16: 2290322240822
                    + 2280422230922
                    step 17: 4570744471744
                    + 4471744470754
                    step 18: 9042488942498
                    + 8942498842409
                    step 19: 17984987784907
                    + 70948778948971
                    step 20: 88933766733878
                    + 87833766733988
                    step 21: 176767533467866
                    + 668764335767671
                    step 22: 845531869235537
                    + 735532968135548
                    step 23: 1581064837371085
                    + 5801737384601851
                    step 24: 7382802221972936
                    + 6392791222082837
                    step 25: 13775593444055773
                    + 37755044439557731
                    step 26: 51530637883613504
                    + 40531638873603515
                    step 27: 92062276757217019
                    + 91071275767226029
                    step 28: 183133552524443048
                    + 840344425255331381
                    step 29: 1023477977779774429
                    + 9244779777797743201
                    step 30: 10268257755577517630
                    + 03671577555775286201
                    step 31: 13939835311352803831
                    + 13830825311353893931
                    step 32: 27770660622706697762
                    + 26779660722606607772
                    step 33: 54550321345313305534
                    + 43550331354312305545
                    step 34: 98100652699625611079
                    + 97011652699625600189
                    step 35: 195112305399251211268
                    + 862112152993503211591
                    step 36: 1057224458392754422859
                    + 9582244572938544227501
                    step 37: 10639469031331298650360
                    + 06305689213313096493601
                    step 38: 16945158244644395143961
                    + 16934159344644285154961
                    step 39: 33879317589288680298922
                    + 22989208688298571397833
                    step 40: 56868526277587251696755
                    + 55769615278577262586865
                    step 41: 112638141556164514283620
                    + 026382415461655141836211
                    step 42: 139020557017819656119831
                    + 138911656918710755020931
                    step 43: 277932213936530411140762
                    + 267041114035639312239772
                    step 44: 544973327972169723380534
                    + 435083327961279723379445
                    step 45: 980056655933449446759979
                    + 979957644944339556650089
                    step 46: 1960014300877789003410068
                    + 8600143009877780034100691
                    step 47: 10560157310755569037510759
                    + 95701573096555701375106501
                    step 48: 106261730407311270412617260
                    + 062716214072113704037162601
                    step 49: 168977944479424974449779861
                    1001699 takes 49 iterations / steps to resolve into a 27 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 2,095,882 times since Saturday, March 9th, 2002.)

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