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  • REVERSAL-ADDITION PALINDROME TEST ON 1007619

    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 1007619:
    1007619
    + 9167001
    step 1: 10174620
    + 02647101
    step 2: 12821721
    + 12712821
    step 3: 25534542
    + 24543552
    step 4: 50078094
    + 49087005
    step 5: 99165099
    + 99056199
    step 6: 198221298
    + 892122891
    step 7: 1090344189
    + 9814430901
    step 8: 10904775090
    + 09057740901
    step 9: 19962515991
    + 19951526991
    step 10: 39914042982
    + 28924041993
    step 11: 68838084975
    + 57948083886
    step 12: 126786168861
    + 168861687621
    step 13: 295647856482
    + 284658746592
    step 14: 580306603074
    + 470306603085
    step 15: 1050613206159
    + 9516023160501
    step 16: 10566636366660
    + 06666363666501
    step 17: 17233000033161
    + 16133000033271
    step 18: 33366000066432
    + 23466000066333
    step 19: 56832000132765
    + 56723100023865
    step 20: 113555100156630
    + 036651001555311
    step 21: 150206101711941
    + 149117101602051
    step 22: 299323203313992
    + 299313302323992
    step 23: 598636505637984
    + 489736505636895
    step 24: 1088373011274879
    + 9784721103738801
    step 25: 10873094115013680
    + 08631051149037801
    step 26: 19504145264051481
    + 18415046254140591
    step 27: 37919191518192072
    + 27029181519191973
    step 28: 64948373037384045
    + 54048373037384946
    step 29: 118996746074768991
    + 199867470647699811
    step 30: 318864216722468802
    + 208864227612468813
    step 31: 527728444334937615
    + 516739433444827725
    step 32: 1044467877779765340
    + 0435679777787644401
    step 33: 1480147655567409741
    + 1479047655567410841
    step 34: 2959195311134820582
    + 2850284311135919592
    step 35: 5809479622270740174
    + 4710470722269749085
    step 36: 10519950344540489259
    + 95298404544305991501
    step 37: 105818354888846480760
    + 067084648888453818501
    step 38: 172903003777300299261
    + 162992003777300309271
    step 39: 335895007554600608532
    + 235806006455700598533
    step 40: 571701014010301207065
    + 560702103010410107175
    step 41: 1132403117020711314240
    + 0424131170207113042311
    step 42: 1556534287227824356551
    1007619 takes 42 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 2,061,757 times since Saturday, March 9th, 2002.)
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