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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 2,061,765 times since Saturday, March 9th, 2002.)
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