山水娱乐

  • REVERSAL-ADDITION PALINDROME TEST ON 1009227

    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 1009227:
    1009227
    + 7229001
    step 1: 8238228
    + 8228328
    step 2: 16466556
    + 65566461
    step 3: 82033017
    + 71033028
    step 4: 153066045
    + 540660351
    step 5: 693726396
    + 693627396
    step 6: 1387353792
    + 2973537831
    step 7: 4360891623
    + 3261980634
    step 8: 7622872257
    + 7522782267
    step 9: 15145654524
    + 42545654151
    step 10: 57691308675
    + 57680319675
    step 11: 115371628350
    + 053826173511
    step 12: 169197801861
    + 168108791961
    step 13: 337306593822
    + 228395603733
    step 14: 565702197555
    + 555791207565
    step 15: 1121493405120
    + 0215043941211
    step 16: 1336537346331
    + 1336437356331
    step 17: 2672974702662
    + 2662074792762
    step 18: 5335049495424
    + 4245949405335
    step 19: 9580998900759
    + 9570098990859
    step 20: 19151097891618
    + 81619879015191
    step 21: 100770976906809
    + 908609679077001
    step 22: 1009380655983810
    + 0183895560839001
    step 23: 1193276216822811
    + 1182286126723911
    step 24: 2375562343546722
    + 2276453432655732
    step 25: 4652015776202454
    + 4542026775102564
    step 26: 9194042551305018
    + 8105031552404919
    step 27: 17299074103709937
    + 73990730147099271
    step 28: 91289804250809208
    + 80290805240898219
    step 29: 171580609491707427
    + 724707194906085171
    step 30: 896287804397792598
    + 895297793408782698
    step 31: 1791585597806575296
    + 6925756087955851971
    step 32: 8717341685762427267
    + 7627242675861437178
    step 33: 16344584361623864445
    + 54446832616348544361
    step 34: 70791416977972408806
    + 60880427977961419707
    step 35: 131671844955933828513
    + 315828339559448176131
    step 36: 447500184515382004644
    + 446400283515481005744
    step 37: 893900468030863010388
    + 883010368030864009398
    step 38: 1776910836061727019786
    + 6879107271606380196771
    step 39: 8656018107668107216557
    + 7556127018667018106568
    step 40: 16212145126335125323125
    + 52132352153362154121261
    step 41: 68344497279697279444386
    1009227 takes 41 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 2,061,754 times since Saturday, March 9th, 2002.)
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