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
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。
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
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}
A^5:
{7351062489, 8105632794, 8401253976, 8731945026, 9164072385, 9238750614, 9615278340,9847103256}
A^4: {5702631489,7264103985,7602314895,7824061395,8105793624,8174035962,8304269175,8904623175,8923670541,9451360827,9785261403,9804753612,9846032571}
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}
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}
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
这个问题15年前曾讨论过： [擂台] Ten digit numbers