这样的A有多少个？

Treenewbee · 发表于 2024-2-9 10:44

n>25时，可以构造一些满足条件的解，但是否最优解，需要去验证，计算量相当可观

王守恩 · 发表于 2024-2-9 16:15

大胆猜测, 小心求证。

B(01)=3=A(00)
B(02)=24,
B(03)=63=A(01)
B(04)=264,
B(05)=1374,
B(06)=3114=A(02)
B(07)=8937=A(03)
B(08)=60663,
B(09)=94863=A(04)
B(10)=545793,
B(11)=1989417,
B(12)=5477133=A(05)
B(13)=20736417,
B(14)=82395387=A(06)
B(15)=260191833,
B(16)=706399164=A(07)
B(17)=2428989417,
B(18)=9380293167=A(08)
B(19)=
B(20)=99497231067=A(09)
B(21)=
B(22)=
B(23)=4472135831667=A(10)
B(24)=
B(25)=62441868958167=A(11)
B(26)=
B(27)=836594274358167=A(12)
B(28)=
B(29)==A(13)
B(30)=
B(31)==A(14)
B(32)=
B(33)==A(15)
B(34)=
B(35)==A(16)
B(36)=
B(37)=
B(38)==A(17)
B(39)=
B(40)==A(18)
B(41)=
B(42)==A(19)
B(43)=
B(44)==A(20)
B(45)=
B(46)==A(21)
B(47)=
B(48)==A(22)
B(49)=
B(50)==A(23)
B(51)=
B(52)==A(24)
B(53)=
B(54)==A(25)
B(55)=
B(56)=
B(57)==A(26)
B(58)=
B(59)==A(27)
B(60)=

王守恩 · 发表于 2024-2-10 08:54

B(01)=3=A(00)
B(02)=24,
B(03)=63=A(01)
B(04)=264,
B(05)=1374,
B(06)=3114=A(02)
B(07)=8937=A(03)
B(08)=60663,
B(09)=94863=A(04)
B(10)=545793,
B(11)=1989417,
B(12)=5477133=A(05)
B(13)=20736417,
B(14)=82395387=A(06)
B(15)=260191833,
B(16)=706399164=A(07)
B(17)=2428989417,
B(18)=9380293167=A(08)
B(19)=28105157886
B(20)=99497231067=A(09)
B(21)=538479339417
B(22)=1974763271886
B(23)=4472135831667=A(10)
B(24)=14106593458167
B(25)=62441868958167=A(11)
B(26)=244744764757083
B(27)=836594274358167=A(12)
B(28)=2445403011773313
B(29)=9983486364492063=A(13)
B(30)=
B(31)==A(14)
B(32)=
B(33)==A(15)
B(34)=
B(35)==A(16)
B(36)=
B(37)=
B(38)==A(17)
B(39)=
B(40)==A(18)
B(41)=
B(42)==A(19)
B(43)=
B(44)==A(20)
B(45)=
B(46)==A(21)
B(47)=
B(48)==A(22)
B(49)=
B(50)==A(23)
B(51)=
B(52)==A(24)
B(53)=
B(54)==A(25)
B(55)=
B(56)=
B(57)==A(26)
B(58)=
B(59)==A(27)
B(60)=

王守恩 · 发表于 2024-2-12 16:10

Treenewbee 发表于 2024-2-9 10:44
n>25时，可以构造一些满足条件的解，但是否最优解，需要去验证，计算量相当可观

我们的算式不能提速吗(还得走这条路)?

n = 1; lst = {}; For[k = 0, k < 10^10, k += 3,
If[Total[IntegerDigits[k^2]] == 9*n, AppendTo[lst, k]; n++]]; lst

复制代码

{3, 24, 63, 264, 1374, 3114, 8937, 60663, 94863, 545793, 1989417, 5477133, 20736417,
82395387, 260191833, 706399164, 2428989417, 9380293167}

3, 24, 63, 264, 1374, 3114, 8937, 60663, 94863, 545793, 1989417, 5477133, 20736417,
82395387, 260191833, 706399164, 2428989417, 9380293167, 28105157886, 99497231067,
538479339417, 1974763271886, 4472135831667, 14106593458167, 62441868958167,
244744764757083, 836594274358167, 2445403011773313, 9983486364492063,

王守恩 · 发表于 2024-2-13 07:59

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)=
B(31)==A(14)
B(32)=
B(33)==A(15)
B(34)=
B(35)==A(16)
B(36)=
B(37)=
B(38)==A(17)
B(39)=
B(40)==A(18)
B(41)=
B(42)==A(19)
B(43)=
B(44)==A(20)
B(45)=
B(46)==A(21)
B(47)=
B(48)==A(22)
B(49)=
B(50)==A(23)
B(51)=
B(52)==A(24)
B(53)=
B(54)==A(25)
B(55)=
B(56)=
B(57)==A(26)
B(58)=
B(59)==A(27)
B(60)=

王守恩 · 发表于 2024-2-13 11:55

Treenewbee 发表于 2024-2-9 10:44
n>25时，可以构造一些满足条件的解，但是否最优解，需要去验证，计算量相当可观

先叉一叉。

\(在n^2这些数里, 可以出现8个9连在一起,9个9连在一起的数吗？\)

王守恩 · 发表于 2024-2-14 16:39

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)==A(14)
B(32)=
B(33)==A(15)
B(34)=
B(35)==A(16)
B(36)=
B(37)=
B(38)==A(17)
B(39)=
B(40)==A(18)
B(41)=
B(42)==A(19)
B(43)=
B(44)==A(20)
B(45)=
B(46)==A(21)
B(47)=
B(48)==A(22)
B(49)=
B(50)==A(23)
B(51)=
B(52)==A(24)
B(53)=
B(54)==A(25)
B(55)=
B(56)=
B(57)==A(26)
B(58)=
B(59)==A(27)
B(60)=

Treenewbee · 发表于 2024-2-15 12:33

王守恩发表于 2024-2-13 11:55
先叉一叉。

\(在n^2这些数里, 可以出现8个9连在一起,9个9连在一起的数吗？\)

n>30之后，毫无悬念会出现的

王守恩 · 发表于 2024-2-16 11:38

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)=546806820540489417=298997698989598998998976689888999889,
A(15)=707106074079263583=499998999999788997978888999589997889,

王守恩 · 发表于 2024-2-18 19:00

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,

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