这样的A有多少个？

northwolves · 发表于 2024-3-16 16:45:13

{1,2,3,5,6,12,9,32,24,53,79,127,116,231,185,492,674,856,831,1606,1482,2482,4305,5823,10409,13933,19749,32086,41688,70342,77538,101742,145602,235353,255052,406517,450252,1017451,696349,994839,2968846,4503178,6206302,7754856,12222592,14831813,26025306,35322773,27746934,70597183,100476671,122323114,87552466,251511047,433525503,661737185,952278002,1077672188}

王守恩 · 发表于 2024-3-16 19:46:21

northwolves 发表于 2024-3-16 16:45
{1,2,3,5,6,12,9,32,24,53,79,127,116,231,185,492,674,856,831,1606,1482,2482,4305,5823,10409,13933,197 ...

119#每串数都可以上OEIS。

王守恩 · 发表于 2024-3-22 17:24:18

先备忘一下。
T(01)=01-0,3^2=9,
      02-?,7=13,
T(02)=03-1,24^2=576,
T(03)=04-1,63^2=3969,
T(04)=05-1,264^2=69696,
      06-?,836=46,
T(05)=07-2,1374^2=1887876,
T(06)=07-1,3114^2=9696996,
T(07)=08-1,8937^2=79869969,
      09-?,29614=70,
T(08)=10-2,60663^2=3679999569,
T(09)=10-1,94863^2=8998988769,
      11-?,298327=89,
T(10)=12-2,545793^2=297889998849,
T(11)=13-2,1989417^2=3957779999889,
T(12)=14-2,5477133^2=29998985899689,
T(13)=15-2,20736417^2=429998989997889,
T(14)=16-2,82395387^2=6788999798879769,
T(15)=17-2,260191833^2=67699789959899889,
T(16)=18-2,706399164^2=498999778899898896,
T(17)=19-2,2428989417^2=5899989587897999889,
T(18)=20-2,9380293167^2=87989899898866889889,
T(19)=21-2,28105157886^2=789899899796987988996,
T(20)=22-2,99497231067^2=9899698989999989958489,
      23-?,244272388937=187,
T(21)=24-3,538479339417^2=289959998978968689899889,
T(22)=25-3,1974763271886^2=3899689979989899957996996,
T(23)=26-3,4472135831667^2=19999998896879889759998889,
T(24)=27-3,14106593458167^2=198995978993999999978999889,
T(25)=28-3,62441868958167^2=3898986998988899589995999889,
T(26)=29-3,244744764757083^2=59899999875999896899998668889,
T(27)=30-3,836594274358167^2=699889979888867998799799599889,
T(28)=31-3,2445403011773313^2=5979995889989989998888898995969,
T(29)=32-3,9983486364492063^2=99669999989998948997699989995969,
      33-?,31622774688331667=271,
T(30)=34-4,44698630849165614^2=1997967599789979898899879999996996,
T(31)=35-4,167032630943744043^2=27899899799988999988898998697985849,
T(32)=36-4,435866837461509417^2=189979899998697868879998999979679889,
T(33)=36-3,707106074079263583^2=499998999999788997978888999589997889,
      37-?,2785480209927724417=301,
T(34)=38-4,5467172934890572764^2=29889979899999998978989858999978599696,
T(35)=39-4,14141782065920722917^2=199989999999996989894777897899888988889,
T(36)=40-4,77453069648658793167^2=5998977997999989949998988998868885889889,
T(37)=41-4,262087386170528775387^2=68689797989699877986999999998989896999769,
T(38)=42-4,754718284918279954614^2=569599689589989999998989999797889899888996,
T(39)=43-4,2827719752694560960583^2=7995998999778988998899699998797979679699889,
T(40)=44-4,8882505274864168010583^2=78898899957989768899997956979998979999999889,
      45-?,24490814584000030724417=367,
T(41)=46-5,43566041821463294027313^2=1897999999989488769979889989869689898789999969,
T(42)=46-4,99689518004050952477133^2=9937999999879998999788999799759989988887899689,
T(43)=47-4,315892386718941028010583^2=99787999986988989979987995998989889798759999889,
T(44)=48-4,893241282627485818275387^2=797879988989995997899989877988999997998969999769,
T(44)=49-?,2999999833333143684778167=396,
T(45)=50-?,9989444428895912224658167=406,
T(46)=51-?,31288943732571046469012083=409,
T(47)=52-5,94815604723008484168010583=423,
T(48)=53-5?
T(49)=54-5?
T(50)=55-5?
T(51)=56-5?
T(52)=57-5?
T(53)=68-5?
T(54)=59-?,314610537013606681884298837387=487,
T(55)=60-5?
T(56)=61-5?
T(57)=62-5,9984988582817657883693383344833=513,
T(58)=63-5?
T(59)=64-5?
T(60)=65-5?
......

northwolves · 发表于 2025-2-8 00:09:40

王守恩发表于 2024-2-28 15:32
先立4根标杆(无限数串, 极限性价比(数码和: 数位)=33:4), 慢慢再来找更好的性价比。
标配11位数。11位数性 ...

这四个无限模式可合并为：

$k=\frac{1}{2}(3 \left((-1)^n+3\right)) 10^{\lfloor \frac{n-1}{2}\rfloor }-\frac{1}{6} \left(10^{\lfloor \frac{n+1}{4}\rfloor -\lfloor \frac{1}{2} \sin \left(\frac{n \pi }{2})\rfloor }+2\right)+6 \lfloor \frac{1}{2} \sin \left(\frac{n \pi }{2}\right)\rfloor$

northwolves · 发表于 2025-2-8 00:12:40

Table[k=(3*(3+(-1)^n))/2*10^Floor[1/2 (-1+n)] -1/6 (10^(Floor[(1+n)/4]-Floor[1/2 Sin[(n \[Pi])/2]])+2)+6 Floor[1/2 Sin[(n \[Pi])/2]];
{n,k,k^2,IntegerLength[k^2],Total@IntegerDigits[k^2]},{n,9,50}]//TableForm

复制代码

9 29983 898980289 9 61
10 59983 3597960289 10 58
11 298327 88998998929 11 88
12 599833 359799627889 12 82
13 2999833 8998998027889 13 94
14 5999833 35997996027889 14 91
15 29983327 898999897988929 15 121
16 59998333 3599799962778889 16 115
17 299998333 89998999802778889 17 127
18 599998333 359997999602778889 18 124
19 2999833327 8998999989779888929 19 154
20 5999983333 35999799996277788889 20 148
21 29999983333 899998999980277788889 21 160
22 59999983333 3599997999960277788889 22 157
23 299998333327 89998999998977798888929 23 187
24 599999833333 359999799999627777888889 24 181
25 2999999833333 8999998999998027777888889 25 193
26 5999999833333 35999997999996027777888889 26 190
27 29999983333327 899998999999897777988888929 27 220
28 59999998333333 3599999799999962777778888889 28 214
29 299999998333333 89999998999999802777778888889 29 226
30 599999998333333 359999997999999602777778888889 30 223
31 2999999833333327 8999998999999989777779888888929 31 253
32 5999999983333333 35999999799999996277777788888889 32 247
33 29999999983333333 899999998999999980277777788888889 33 259
34 59999999983333333 3599999997999999960277777788888889 34 256
35 299999998333333327 89999998999999998977777798888888929 35 286
36 599999999833333333 359999999799999999627777777888888889 36 280
37 2999999999833333333 8999999998999999998027777777888888889 37 292
38 5999999999833333333 35999999997999999996027777777888888889 38 289
39 29999999983333333327 899999998999999999897777777988888888929 39 319
40 59999999998333333333 3599999999799999999962777777778888888889 40 313
41 299999999998333333333 89999999998999999999802777777778888888889 41 325
42 599999999998333333333 359999999997999999999602777777778888888889 42 322
43 2999999999833333333327 8999999998999999999989777777779888888888929 43 352
44 5999999999983333333333 35999999999799999999996277777777788888888889 44 346
45 29999999999983333333333 899999999998999999999980277777777788888888889 45 358
46 59999999999983333333333 3599999999997999999999960277777777788888888889 46 355
47 299999999998333333333327 89999999998999999999998977777777798888888888929 47 385
48 599999999999833333333333 359999999999799999999999627777777777888888888889 48 379
49 2999999999999833333333333 8999999999998999999999998027777777777888888888889 49 391
50 5999999999999833333333333 35999999999997999999999996027777777777888888888889 50 388

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[灌水] 这样的A有多少个？

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