这样的A有多少个？

王守恩

谢谢 mathe 版主！！！

A(00)=3=9,
B(02)=24=576,
A(01)=63=3969,
B(04)=264=69696,
B(05)=1374=1887876,
A(02)=3114=9696996,
A(03)=8937=79869969,
B(08)=60663=3679999569,
A(04)=94863=8998988769,
B(10)=545793=297889998849,
B(11)=1989417=3957779999889,
A(05)=5477133=29998985899689,
B(13)=20736417=429998989997889,
A(06)=82395387=6788999798879769,
B(15)=260191833=67699789959899889,
A(07)=706399164=498999778899898896,
B(17)=2428989417= 5899989587897999889,
A(08)=9380293167=87989899898866889889,
B(19)=28105157886=789899899796987988996,
A(09)=99497231067=9899698989999989958489,
B(21)=538479339417=289959998978968689899889,
B(22)=1974763271886=3899689979989899957996996,
A(10)=4472135831667=19999998896879889759998889,
B(24)=14106593458167=198995978993999999978999889,
A(11)=62441868958167=3898986998988899589995999889,
B(26)=244744764757083=59899999875999896899998668889,
A(12)=836594274358167=699889979888867998799799599889,
B(28)=2445403011773313=5979995889989989998888898995969,
A(13)=9983486364492063=99669999989998948997699989995969,
B(30)=44698630849165614=1997967599789979898899879999996996,
B(31)=167032630943744043=27899899799988999988898998697985849,
A(14)=435866837461509417=189979899998697868879998999979679889,
A(15)=707106074079263583=499998999999788997978888999589997889,
B(34)=5467172934890572764=29889979899999998978989858999978599696,
A(16)=14141782065920722917=199989999999996989894777897899888988889,
B(36)=77453069648658793167=5998977997999989949998988998868885889889,
B(37)=262087386170528775387=68689797989699877986999999998989896999769,
A(17)=754718284918279954614=569599689589989999998989999797889899888996,
B(39)=2827719752694560960583=7995998999778988998899699998797979679699889,
A(18)=8882505274864168010583=78898899957989768899997956979998979999999889,

王守恩

王守恩 发表于 2024-2-13 11:55
先叉一叉。

\(在n^2这些数里,  可以出现8个9连在一起,9个9连在一起的数吗？\)

583^2=339889, 40/06=6.666666
59833^2=3579987889, 73/10=7.300000
5998333^2=35979998778889,106 /14=7.571428
599983333^2=359979999877788889, 139/18=7.722222
59999833333^2=3599979999987777888889, 172/22=7.818181
5999998333333^2=35999979999998777778888889, 205/26=7.884615
规律:  (40+33n)/(6+4n)=8.25+。

王守恩

Treenewbee 发表于 2024-2-15 12:33
n>30之后，毫无悬念会出现的

298327^2=88998998929,
29983327^2=898999897988929,
2999833327^2=8998999989779888929,
299998333327^2=89998999998977798888929,
29999983333327^2=
2999999833333327^2=
299999998333333327^2
......
求助：这电脑应该怎样编排？

\(\sqrt{10}=3.1622776601683793319988935444327185337195551393252\)

31^2=961,
316^2=99856,
3162^2=9998244,
31622^2=999950884,
316227^2=99999515529,
3162277^2=9999995824729,
31622776^2=999999961946176,
......
这电脑又该怎样编排？

Treenewbee

1. Table[{Floor@Sqrt[10^(2n-1)],Floor[Sqrt[10^(2n-1)]]^2},{n,20}]//TableForm

复制代码

3        9
31        961
316        99856
3162        9998244
31622        999950884
316227        99999515529
3162277        9999995824729
31622776        999999961946176
316227766        99999999989350756
3162277660        9999999998935075600
31622776601        999999999956753113201
316227766016        99999999999470044512256
3162277660168        9999999999997600893788224
31622776601683        999999999999949826038432489
316227766016837        99999999999999409792567484569
3162277660168379        9999999999999997900254631487641
31622776601683793        999999999999999979762122758866849
316227766016837933        99999999999999999873578871987712489
3162277660168379331        9999999999999999993682442519108007561
31622776601683793319        999999999999999999937454230741109035761

Treenewbee

1. Table[k=3*10^(2n-1)-(5*10^n+19)/3;{k,k^2},{n,20}]//TableForm

复制代码

7        49
2827        7991929
298327        88998998929
29983327        898999897988929
2999833327        8998999989779888929
299998333327        89998999998977798888929
29999983333327        899998999999897777988888929
2999999833333327        8999998999999989777779888888929
299999998333333327        89999998999999998977777798888888929
29999999983333333327        899999998999999999897777777988888888929
2999999999833333333327        8999999998999999999989777777779888888888929
299999999998333333333327        89999999998999999999998977777777798888888888929
29999999999983333333333327        899999999998999999999999897777777777988888888888929
2999999999999833333333333327        8999999999998999999999999989777777777779888888888888929
299999999999998333333333333327        89999999999998999999999999998977777777777798888888888888929
29999999999999983333333333333327        899999999999998999999999999999897777777777777988888888888888929
2999999999999999833333333333333327        8999999999999998999999999999999989777777777777779888888888888888929
299999999999999998333333333333333327        89999999999999998999999999999999998977777777777777798888888888888888929
29999999999999999983333333333333333327        899999999999999998999999999999999999897777777777777777988888888888888888929
2999999999999999999833333333333333333327        8999999999999999998999999999999999999989777777777777777779888888888888888888929

王守恩

Treenewbee 发表于 2024-2-23 11:33
7        49
2827        7991929
298327        88998998929

1. Table[k = 6*10^(2 n) - (5*10^n + 1)/3; {k, k^2}, {n, 20}] // TableForm

复制代码

{"583", "339889"},
{"59833", "3579987889"},
{"5998333", "35979998778889"},
{"599983333", "359979999877788889"},
{"59999833333", "3599979999987777888889"},
{"5999998333333", "35999979999998777778888889"},
{"599999983333333", "359999979999999877777788888889"},
{"59999999833333333", "3599999979999999987777777888888889"},
{"5999999998333333333", "35999999979999999998777777778888888889"},
{"599999999983333333333",
359999999979999999999877777777788888888889,
{"59999999999833333333333",
3599999999979999999999987777777777888888888889,
{"5999999999998333333333333",
35999999999979999999999998777777777778888888888889,
{"599999999999983333333333333",
359999999999979999999999999877777777777788888888888889,
{"59999999999999833333333333333",
3599999999999979999999999999987777777777777888888888888889,
{"5999999999999998333333333333333",
35999999999999979999999999999998777777777777778888888888888889,
{"599999999999999983333333333333333",
359999999999999979999999999999999877777777777777788888888888888889,
{"59999999999999999833333333333333333",
3599999999999999979999999999999999987777777777777777888888888888888889,
{"5999999999999999998333333333333333333",
35999999999999999979999999999999999998777777777777777778888888888888888889,
{"599999999999999999983333333333333333333",
359999999999999999979999999999999999999877777777777777777788888888888888888889,

Treenewbee

Treenewbee 发表于 2024-2-23 11:25
3        9
31        961
316        99856

前10000项比值>7.2的只有以下几项：{1, 3, 9, 15, 17, 18}

Treenewbee

Treenewbee 发表于 2024-2-23 14:31
前10000项比值>7.2的只有以下几项：{1, 3, 9, 15, 17, 18}

46楼比值与最小n:
{8.230, 119}, {8.231, 125}, {8.232, 132}, {8.233, 140}, {8.234, 148},{8.235, 158}, {8.236, 170}, {8.237, 183}, {8.238, 198}, {8.239, 216},{8.24, 237}, {8.241, 264}, {8.242, 297}, {8.243, 339}, {8.244, 396}, {8.245, 475}, {8.246, 594}, {8.247, 792},{8.248, 1187}, {8.249, 2375},{8.24976,10^4},{8.24998,10^5},{8.249997625,10^6},{8.249999763,10^7},{8.24999997625,10^8}

王守恩

Treenewbee 发表于 2024-2-23 15:51
46楼比值与最小n:
{8.230, 119}, {8.231, 125}, {8.232, 132}, {8.233, 140}, {8.234, 148},{8.235, 158 ...

45#,46#极限比值=33/4, 比值≥33/4的平方数, 我只有这么1个(接41#),
B(44)=A(20)=893241282627485818275387^2
=797879988989995997899989877988999997998969999769=44*9/48=33/4
谢谢 mathe 版主！！！谢谢！

王守恩

A=十位数，由0,1,2,3,4,5,6,7,8,9组成，
A^2=二十位数，由0,0,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9组成。
这样的A有多少个？