3^n倍数的n位数

王守恩

A(n)=十进制的n位数,  每个数位只由数码 2,3,4,5 构成,   A(n)是3^n的倍数。譬如
A(1)=3,
A(2)=45,
A(3)=243,
A(4)=4455,
A(5)=24543,
A(6)=222345, ——有多个解时取最小的那个。
A(7)=3444525,
A(8)=23324355,
A(9)=225252252,

Table[SelectFirst[FromDigits /@ Tuples[{2, 3, 4, 5}, n], Mod[#, 3^n] == 0 &], {n, 9}]

我只会用这个。大了就来不了。各位大侠！再来几个开开眼。谢谢！！！

王守恩

A(n)=十进制的n位数, 且A(n)是3^n的倍数。 每个数位只由9个数码(1—9)中的4个不同数码构成, 可以有74个组合。——明显无解的已删除。——不知这74个组合是否都"有解"？——疑惑？
{1236}, {1239}, {1249}, {1259}, {1267}, {1268}, {1269}, {1279}, {1289}, {1345},
{1349}, {1356}, {1358}, {1359}, {1369}, {1378}, {1379}, {1389}, {1459}, {1468},
{2378}, {1469}, {1479}, {1489}, {1569}, {1579}, {1589}, {1679}, {1689}, {1789},
{2345}, {2346}, {2347}, {2349}, {2359}, {2369}, {2379}, {2389}, {2459}, {2469},
{2479}, {2489}, {2567}, {2569}, {2579}, {2589}, {2679}, {2689}, {2789}, {3459},
{3468}, {3469}, {3479}, {3489}, {3567}, {3569}, {3579}, {3589}, {3678}, {3679},
{3689}, {3789}, {4567}, {4568}, {4569}, {4579}, {4589}, {4679}, {4689}, {4789},
{5679}, {5689}, {5789}, {6789},

同上,   9不能有,   可以有18个组合。
{1236}, {1267}, {1268}, {1345}, {1356}, {1358},
{1378}, {1468}, {2378}, {2345}, {2346}, {2347},
{2567}, {3468}, {3469}, {3567}, {4567}, {4568},

同上,   9与6都不能有,   只有6个组合。
A{1345}={3, 45, 135, 1134, 33534, 114453, 1454355, 11114334, 113531544, 1133445555, 11533155435, 113315444343}
A{1358}={3, 18, 135, 3888, 13851, 188811, 1113183, 11383335, 113885838, 1355883138, 11538115551, 111835381158}——这串数可以无限长叫"有解"。
A{1378}={3, 18, 378, 1377, 11178, 137781, 1113183, 11173383, 137111778, 1171118817, 13177788183, 111173737113}
A{2378}={3, 27, 378, 3888, 23328, 238383, 2283228, 27838323, 222732828, 2327888727, 22722822837, 222783787287}——再长我就来不了了——各位大侠！再长几个开开眼。谢谢！！！
A{2345}={3, 45, 243, 4455, 24543, 222345, 3444525, 23324355, 225252252, 2432523555, 22223445444, 225242233353}
A{2347}={3, 27, 243, 4374, 33777, 332424, 2342277, 23337477, 322427223, 2344422447, 22477474242, 244224774432}——OEIS可是没有这些数字串的。