山水娱乐

  • REVERSAL-ADDITION PALINDROME TEST ON 11979990

    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 11979990:
    11979990
    + 09997911
    step 1: 21977901
    + 10977912
    step 2: 32955813
    + 31855923
    step 3: 64811736
    + 63711846
    step 4: 128523582
    + 285325821
    step 5: 413849403
    + 304948314
    step 6: 718797717
    + 717797817
    step 7: 1436595534
    + 4355956341
    step 8: 5792551875
    + 5781552975
    step 9: 11574104850
    + 05840147511
    step 10: 17414252361
    + 16325241471
    step 11: 33739493832
    + 23839493733
    step 12: 57578987565
    + 56578987575
    step 13: 114157975140
    + 041579751411
    step 14: 155737726551
    + 155627737551
    step 15: 311365464102
    + 201464563113
    step 16: 512830027215
    + 512720038215
    step 17: 1025550065430
    + 0345600555201
    step 18: 1371150620631
    + 1360260511731
    step 19: 2731411132362
    + 2632311141372
    step 20: 5363722273734
    + 4373722273635
    step 21: 9737444547369
    + 9637454447379
    step 22: 19374898994748
    + 84749989847391
    step 23: 104124888842139
    + 931248888421401
    step 24: 1035373777263540
    + 0453627773735301
    step 25: 1489001550998841
    + 1488990551009841
    step 26: 2977992102008682
    + 2868002012997792
    step 27: 5845994115006474
    + 4746005114995485
    step 28: 10591999230001959
    + 95910003299919501
    step 29: 106502002529921460
    + 064129925200205601
    step 30: 170631927730127061
    + 160721037729136071
    step 31: 331352965459263132
    + 231362954569253133
    step 32: 562715920028516265
    + 562615820029517265
    step 33: 1125331740058033530
    + 0353308500471335211
    step 34: 1478640240529368741
    + 1478639250420468741
    step 35: 2957279490949837482
    + 2847389490949727592
    step 36: 5804668981899565074
    + 4705659981898664085
    step 37: 10510328963798229159
    + 95192289736982301501
    step 38: 105702618700780530660
    + 066035087007816207501
    step 39: 171737705708596738161
    + 161837695807507737171
    step 40: 333575401516104475332
    + 233574401615104575333
    step 41: 567149803131209050665
    + 566050902131308941765
    step 42: 1133200705262517992430
    + 0342997152625070023311
    step 43: 1476197857887588015741
    + 1475108857887587916741
    step 44: 2951306715775175932482
    + 2842395715775176031592
    step 45: 5793702431550351964074
    + 4704691530551342073975
    step 46: 10498393962101694038049
    + 94083049610126939389401
    step 47: 104581443572228633427450
    + 054724336822275344185401
    step 48: 159305780394503977612851
    + 158216779305493087503951
    step 49: 317522559699997065116802
    + 208611560799996955225713
    step 50: 526134120499994020342515
    + 515243020499994021431625
    step 51: 1041377140999988041774140
    + 0414771408899990417731401
    step 52: 1456148549899978459505541
    + 1455059548799989458416541
    step 53: 2911208098699967917922082
    + 2802297197699968908021192
    step 54: 5713505296399936825943274
    + 4723495286399936925053175
    step 55: 10437000582799873750996449
    + 94469905737899728500073401
    step 56: 104906906320699602251069850
    + 058960152206996023609609401
    step 57: 163867058527695625860679251
    + 152976068526596725850768361
    step 58: 316843127054292351711447612
    + 216744117153292450721348613
    step 59: 533587244207584802432796225
    + 522697234208485702442785335
    step 60: 1056284478416070504875581560
    + 0651855784050706148744826501
    step 61: 1708140262466776653620408061
    + 1608040263566776642620418071
    step 62: 3316180526033553296240826132
    + 2316280426923553306250816133
    step 63: 5632460952957106602491642265
    + 5622461942066017592590642365
    step 64: 11254922895023124195082284630
    + 03648228059142132059822945211
    step 65: 14903150954165256254905229841
    + 14892250945265256145905130941
    step 66: 29795401899430512400810360782
    + 28706301800421503499810459792
    step 67: 58501703699852015900620820574
    + 47502802600951025899630710585
    step 68: 106004506300803041800251531159
    + 951135152008140308003605400601
    step 69: 1057139658308943349803856931760
    + 0671396583089433498038569317501
    step 70: 1728536241398376847842426249261
    + 1629426242487486738931426358271
    step 71: 3357962483885863586773852607532
    + 2357062583776853685883842697533
    step 72: 5715025067662717272657695305065
    + 5605035967562727172667605205175
    step 73: 11320061035225444445325300510240
    + 04201500352354444452253016002311
    step 74: 15521561387579888897578316512551
    11979990 takes 74 iterations / steps to resolve into a 32 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 2,061,808 times since Saturday, March 9th, 2002.)
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