这样的A有多少个？

northwolves

A164841                Numbers whose squares have a digit average greater than 8.               

3, 94863, 987917, 3162083, 29983327, 99477133, 99483667, 994927133, 2428989417, 2754991833, 2983284917, 2999833327, 3157196367, 9380293167, 9486778167, 28105157886, 31144643167, 31304790167, 31459487917, 31464263856, 94286790167, 99497231067, 244272388937

王守恩

northwolves 发表于 2024-2-24 14:17
A164841                Numbers whose squares have a digit average greater than 8.               

3, 94863, 987917, 3162083, 29 ...

放松放松。

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？OEIS没有的！我好不容易找了1个：7839425610^2=61456593894723872100。

northwolves

A164772                Numbers n with property that average digit of n^2 is s=8.       

313, 298327, 9893887, 197483417, 282753937, 314623583, 315432874, 706399164, 773303937, 894303633, 947047833, 948675387, 989938887, 994987437, 998398167, 8882454614, 8888194417, 8943142063, 9374913167, 9416989417, 9476286187, 9949260676, 9949823114

northwolves

王守恩 发表于 2024-2-24 15:26
放松放松。

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, ...

这种解很多，比如满足条件的A^6:

{7025869314, 7143258096, 7931584062, 8094273561, 8920416357, 9247560381}

northwolves

A^5:

{7351062489, 8105632794, 8401253976, 8731945026, 9164072385, 9238750614, 9615278340,  9847103256}

northwolves

A^4: {5702631489,7264103985,7602314895,7824061395,8105793624,8174035962,8304269175,8904623175,8923670541,9451360827,9785261403,9804753612,9846032571}

northwolves

A^3: {4680215379,4752360918,4765380219,4915280637,5063248197,5164738920,5382417906,5426370189,5429013678,5628130974,5679321048,5697841320,5762831940,5783610492,5786430129,5903467821,6019285734,6053147982,6095721483,6143720958,6158723094,6270841539,6295873401,6320184579,6351072984,6403859217,6429053817,6482357019,6487213905,6523710849,6705293418,6804793512,6829053147,6835274091,6857023419,7103895462,7105368294,7138509642,7251639804,7269184530,7295106438,7304291685,7403591286,7409658231,7459102386,7513968420,7538194206,7596214803,7619523048,7648130925,7891406235,7912308456,7945163082,7964025813,7980154263,8092146573,8269417305,8349570621,8469257031,8579462103,8769350412,9047813256,9075346128,9084371562,9216385407,9267083541,9306125487,9470156823,9483672015,9502148376,9563714028,9568042317,9754012836,9863527104}

northwolves

n=1 to 6 有解：

最小十位数: {1023456789, 3164078925, 4680215379, 5702631489, 7351062489, 7025869314}
最大十位数: {9876543210, 9876153024, 9846352710, 9846032571, 9847103256, 9247560381}

northwolves

A357755                Number of solutions for a 10-digit number whose n-th power contains each digit (0-9) exactly n times.       

3265920, 468372, 65663, 15487, 5020, 1930, 855, 417, 246, 114, 97, 45, 33, 24, 20, 18, 7, 6, 1, 3, 2, 3, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1

northwolves

这个问题15年前曾讨论过： [擂台] Ten digit numbers