(k1)^3+(k2)^3+(k3)^3=n^3

王守恩

northwolves 发表于 2026-1-11 10:03
{1,{{a->4,b->4,c->6,d->7}}}
{2,{{a->2,b->43,c->58,d->65}}}
{3,{{a->15,b->385,c->499,d->566}}}

Do[Print[{n, FindInstance[{a^3 + b^3 + c^3 - d^3 == n, 0 ≤ a ≤ b ≤ c ≤ d ≤ Infinity}, {a, b, c, d}, Integers]}], {n, 30}]——这个不听话——就想看看4立方的威力——少走弯路！！！

这个代码答案不好复制——我还是喜欢{n,a,b,c,d},{n,a,b,c,d},...{n,a,b,c,d}——1长行模式——不会用。——编码这块我是完全放弃了。人贵有自知之明。

王守恩

接29#。

{0, 1, -1, 0, 0, 0},
{1, 1, -1, 0, 0, 1},
{2, 0, -5, -4, -4, -1},
{3, 0, -5, -4, -4, 0},
{4, 0, -5, -4, -4, 1},
{5, 2, 0, 1, 1, -1},
{6, 2, 0, 1, 1, 0},
{7, 2, 0, 1, 1, 1},
{8, 1, -3, -3, -2, -1},
{9, 1, -3, -3, -2, 0},
{10, 1, -3, -3, -2, 1},
{11, 3, 1, 2, 2, -1},
{12, 3, 1, 2, 2, 0},
{13, 3, 1, 2, 2, 1},
{14, 2, -1, -2, 0, -1},
{15, 2, -1, -2, 0, 0},
{16, 2, -1, -2, 0, 1},
{17, 4, 2, 3, 3, -1},
{18, 4, 2, 3, 3, 0},
{19, 4, 2, 3, 3, 1},
{20, 3, 1, -1, 2, -1},
{21, 3, 1, -1, 2, 0},
{22, 3, 1, -1, 2, 1},
{23, 5, 3, 4, 4, -1},
{24, 5, 3, 4, 4, 0},
{25, 5, 3, 4, 4, 1},
{26, 4, 3, 0, 4, -1},
{27, 4, 3, 0, 4, 0},
{28, 4, 3, 0, 4, 1},
{29, 6, 4, 5, 5, -1},
{30, 6, 4, 5, 5, 0},
{31, 6, 4, 5, 5, 1},
{32, 5, 5, 1, 6, -1},
{33, 5, 5, 1, 6, 0},
{34, 5, 5, 1, 6, 1},
{35, 7, 5, 6, 6, -1},
{36, 7, 5, 6, 6, 0},
{37, 7, 5, 6, 6, 1},
{38, 6, 7, 2, 8, -1},
{39, 6, 7, 2, 8, 0},
{40, 6, 7, 2, 8, 1},
{41, 8, 6, 7, 7, -1},
{42, 8, 6, 7, 7, 0},
{43, 8, 6, 7, 7, 1},
{44, 7, 9, 3, 10, -1},
{45, 7, 9, 3, 10, 0},
{46, 7, 9, 3, 10, 1},
{47, 9, 7, 8, 8, -1},
{48, 9, 7, 8, 8, 0},
{49, 9, 7, 8, 8, 1},
{50, 8, 11, 4, 12, -1},
{51, 8, 11, 4, 12, 0},
{52, 8, 11, 4, 12, 1},
{53, 10, 8, 9, 9, -1},
{54, 10, 8, 9, 9, 0},
{55, 10, 8, 9, 9, 1},
{56, 9, 13, 5, 14, -1},
{57, 9, 13, 5, 14, 0},
{58, 9, 13, 5, 14, 1},
{59, 11, 9, 10, 10, -1},
{60, 11, 9, 10, 10, 0},
{61, 11, 9, 10, 10, 1},
{62, 10, 15, 6, 16, -1},
{63, 10, 15, 6, 16, 0},
{64, 10, 15, 6, 16, 1},
{65, 12, 10, 11, 11, -1},
{66, 12, 10, 11, 11, 0},
{67, 12, 10, 11, 11, 1},
{68, 11, 17, 7, 18, -1},
{69, 11, 17, 7, 18, 0},
{70, 11, 17, 7, 18, 1},
{71, 13, 11, 12, 12, -1},
{72, 13, 11, 12, 12, 0},
{73, 13, 11, 12, 12, 1},
{74, 12, 19, 8, 20, -1},
{75, 12, 19, 8, 20, 0},
{76, 12, 19, 8, 20, 1},
{77, 14, 12, 13, 13, -1},
{78, 14, 12, 13, 13, 0},
{79, 14, 12, 13, 13, 1},
{80, 13, 21, 9, 22, -1},
{81, 13, 21, 9, 22, 0},
{82, 13, 21, 9, 22, 1},
{83, 15, 13, 14, 14, -1},
{84, 15, 13, 14, 14, 0},
{85, 15, 13, 14, 14, 1},
{86, 14, 23, 10, 24, -1},
{87, 14, 23, 10, 24, 0},
{88, 14, 23, 10, 24, 1},
{89, 16, 14, 15, 15, -1},
{90, 16, 14, 15, 15, 0},
{91, 16, 14, 15, 15, 1},
{92, 15, 25, 11, 26, -1},
{93, 15, 25, 11, 26, 0},
{94, 15, 25, 11, 26, 1},
{95, 17, 15, 16, 16, -1},
{96, 17, 15, 16, 16, 0},
{97, 17, 15, 16, 16, 1},
{98, 16, 27, 12, 28, -1},
{99, 16, 27, 12, 28, 0},
{100, 16, 27, 12, 28, 1},

Table[With[{m = Quotient[n + 1, 6], r = Mod[n, 6]}, If[r < 2 || r == 5, {n, m + 1, m - 1, m, m, If[r == 5, -1, r]}, {n, m, 2 m - 5, m - 4, 2 m - 4, r - 3}]], {n, 0, 100}]

王守恩

\(00=1^3-1^3-0^3-0^3-0^3\)
\(01=1^3-1^3-0^3-0^3+1^3\)
\(02=0^3-5^3+4^3+4^3-1^3\)
\(03=0^3-5^3+4^3+4^3-0^3\)
\(04=0^3-5^3+4^3+4^3+1^3\)
\(05=2^3+0^3-1^3-1^3-1^3\)
\(06=2^3+0^3-1^3-1^3-0^3\)
\(07=2^3+0^3-1^3-1^3+1^3\)
\(08=1^3-3^3+3^3+2^3-1^3\)
\(09=1^3-3^3+3^3+2^3-0^3\)
\(10=1^3-3^3+3^3+2^3+1^3\)
\(11=3^3+1^3-2^3-2^3-1^3\)
\(12=3^3+1^3-2^3-2^3-0^3\)
\(13=3^3+1^3-2^3-2^3+1^3\)
\(14=2^3-1^3+2^3-0^3-1^3\)
\(15=2^3-1^3+2^3-0^3-0^3\)
\(16=2^3-1^3+2^3-0^3+1^3\)
\(17=4^3+2^3-3^3-3^3-1^3\)
\(18=4^3+2^3-3^3-3^3-0^3\)
\(19=4^3+2^3-3^3-3^3+1^3\)
\(20=3^3+1^3+1^3-2^3-1^3\)
\(21=3^3+1^3+1^3-2^3-0^3\)
\(22=3^3+1^3+1^3-2^3+1^3\)
\(23=5^3+3^3-4^3-4^3-1^3\)
\(24=5^3+3^3-4^3-4^3-0^3\)
\(25=5^3+3^3-4^3-4^3+1^3\)
\(26=4^3+3^3-0^3-4^3-1^3\)
\(27=4^3+3^3-0^3-4^3-0^3\)
\(28=4^3+3^3-0^3-4^3+1^3\)
\(29=6^3+4^3-5^3-5^3-1^3\)
\(30=6^3+4^3-5^3-5^3-0^3\)
\(31=6^3+4^3-5^3-5^3+1^3\)
\(32=5^3+5^3-1^3-6^3-1^3\)
\(33=5^3+5^3-1^3-6^3-0^3\)
\(34=5^3+5^3-1^3-6^3-1^3\)
\(35=7^3+5^3-6^3-6^3-1^3\)
\(36=7^3+5^3-6^3-6^3-0^3\)
\(37=7^3+5^3-6^3-6^3+1^3\)
\(38=6^3+7^3-2^3-8^3-1^3\)
\(39=6^3+7^3-2^3-8^3-0^3\)
\(40=6^3+7^3-2^3-8^3+1^3\)
\(41=8^3+6^3-7^3-7^3-1^3\)
\(42=8^3+6^3-7^3-7^3-0^3\)
\(43=8^3+6^3-7^3-7^3+1^3\)

我们能把"1"去掉吗？？？——去不了, 丢一丢。

把1个正整数拆分成4个整数的立方和。——有个方法,不妨试一试。

譬如：\(m=10,10n=b^3+c^3+d^3,n=1,2,3,4,5,6,7,8,9,......\)都有解。则
\(10m+0=10(m+0)+0^3\)
\(10m+1=10(m+0)+1^3\)
\(10m+2=10(m+1)-2^3\)
\(10m+3=10(m+3)-3^3\)
\(10m+4=10(m-6)+4^3\)
\(10m+5=10(m-12)+5^3=10(m+13)-5^3=10(m+12)-5^3=10(m-13)+5^3\)
\(10m+6=10(m+7)-4^3\)
\(10m+7=10(m-2)+3^3\)
\(10m+8=10(m-0)+2^3\)
\(10m+9=10(m+1)-1^3\)

只要m属于这串数——{1, 2, 3, 5, 6, 10, 11, 15, 17, 22, 23, 29, 30, 33, 34, 41, 46, 47, 51, 53, 55, 58, 59, 66, 69, 71, 82, 83, 85, 87, 89, 94, 101, 102, 106, 107, 110, 113, 115, 118, 123, 131, 137, 138, 141, 142}——“4立方和”就解决了。

  10n——不好找。  9n——好找, 可惜不属于这串数。

Flatten@ParallelTable[d /. FindInstance[{10 n == b^3 + c^3 + d^3, b <= c <= d <= 10002}, {b, c, d}, Integers, 1], {n, 1000}]
{2, 3, d, d, d, 5, 20, 8, 6, 7, d, 4, d, d, 317, 6, 9, d, 9, 6, 7, d, d, 29, 5, 12, 6, 7, d, 55, d, d, 11, 6, 7, 8, 7, 7, d, d, d, d, 29, 8, 9, 7, 7, 10, d, d, 8, 8, d, 9, 13, 9, 529, d, d, d, 8, 26, 10, 8, 13, d, d, d, 164, 14, 9, 9, 9, 12, 7, d,
d, 32, 9, 14, 21, 9, d, 16, d, d, d, d, 14, 33, 35, 18, 13, d, d, 8, 45, 8, 11, 12, d, d, d, d, d, 11, 9, 9, 31, 67, d, d, d, 20, 2753, 17, 13, 40, 21, 634, d, d, d, 9, 10, 12, 11, 12, d, d, d, d, 11, 11, 11, 15, 10, 16, d, d, 53, 87, 39, 14,
9, 13, 3079, d, d, 11, 12, 12, 17, 13, 43, 13, d, d, d, 12, 11, 15, 12, 28, 13, d, d, 14, 15, 12, 57, 14, 12, 4093, d, d, d, 539, 13, 12, 13, 196, 9076, d, d, d, 11, 12, 14, 16, 49, 58, d, d, 26, 14, 9, 15, 15, 10, 19, d, d, 884, 17, 11,
13, 13, 874, 9754, d, d, d, 14, 11, 13, 13, 3007, 13, d, d, d, 4178, 14, 15, 15, 28, 2128, d, d, 1169, d, 13, 637, 56, 16, d, d, d, 14, 21, 19, 15, 13, 27, d, d, d, 1433, 15, 125, 15, 25, 13, d, d, d, d, 56, 130, 30, 14, d, 16, d, d, 11,
14, 14, 21, 15, 12, 133, d, d, 14, 14, 17, 19, 14, d, 145, d, d, 23, 33, 14, 16, 15, 4762, 460, d, d, d, 32, 14, 23, d, 13, 10, d, d, 62, 15, 45, 14, 17, 16, d, d, d, d, 14, 1595, 1136, 15, 13, d, d, d, 7409, 65, 16, 12, 15, 9231, d, d,
d, 6455, 15, 14, d, 15, 40, 58, d, d, d, 66, 15, 19, 14, 15, 25, d, d, 44, 38, 14, 18, 13, 438, 13, d, d, 17, 23, 15, 18, 14, 25, d, d, d, 167, d, 14, 32, 19, 15, 22, d, d, 47, 14, 41, 16, 22, 13, d, d, d, 20, 1100, 15, 68, 16, 115, 3250,
d, d, d, 17, 14, 14, 16, d, 19, d, d, d, d, 15, 13, 67, 16, 16, d, d, 236, 17, 21, 23, 16, 16, d, d, d, 14, 51, 16, 15, 19, 15, d, d, d, 47, 35, 98, 15, 13, 21, d, d, d, d, 12, 17, 363, 39, 1525, 16, d, d, d, 14, 15, 15, 23, 34, 1789, d, d,
548, 17, 39, 24, 16, 13, d, d, d, d, 83, 17, 26, 19, 16, 31, d, d, 44, 20, 15, 15, 17, 39, 796, d, d, 770, 18, 17, 21, 45, 16, 31, d, d, 17, 273, 14, 16, 19, 70, d, d, d, 89, 485, 17, 17, d, 15, 499, d, d, d, 48, 16, 15, 42, 2281, 16, d,
d, d, 26, 35, 90, 18, 94, d, d, d, d, 21, 17, 17, 17, d, 22, d, d, 53, 215, 15, 16, 26, 43, d, d, d, 17, d, 14, 18, 40, 42, 19, d, d, 17, 30, 17, 15, 73, 28, 22, d, d, 2156, 17, 27, 14, 18, 34, d, d, d, 17, 143, 15, 16, 16, 145, 115, d, d,
23, 18, 16, d, 18, d, 5635, d, d, d, 24, 18, 17, 16, 18, d, d, d, 14, 164, 29, 156, 16, 18, d, d, d, 47, 7968, 17, 15, 19, 16, d, d, d, 17, 119, 14, 23, 55, 5173, 64, d, d, 89, 18, d, 18, 81, 16, d, d, d, d, 77, 3005, 19, 28, 28, d, d, d,
d, 17, 29, 42, 21, d, d, d, d, d, 482, 17, 24, 19, 25, 34, d, d, 65, 17, 29, 1709, 19, 30, 19, d, d, 32, 7526, 23, 15, 24, 27, d, d, d, 68, 18, 47, 16, 19, 19, d, d, d, 2219, 1049, 19, 21, 46, 19, d, d, d, 41, 20, 18, 27, 49, d, d, d, d,
53, 24, 541,17, 22, 19, 364, d, d, 113, d, 18, 19, 19, d, 3949, d, d, 113, 20, 21, 18, 15, 25, 601, d, d, 29, 36, 17, 57, 75, 40, 1378, d, d, 26, 15, 24, 16, 20, 19, 25, d, d, d, 53, 4773, 18, 421, 19, d, d, d, 41,17, 806, 32, 30, 6877,
16, d, d, 809, 20, 564, 356, 15, 82, 37, d, d, d, 42, 43, 195, 16, d, 19, d, d, 32, d, 35, 22, 21, 403, d, d, d, 203, 2151, 17, 74, 21,18, 682, d, d, 23, 50, d, 19, 17, 21, d, d, d, d, 36, 1550, 19, 16, 52, d, d, d, 20, 21, 53, 17, 37, 52,
478, d, d, 65, 57, 18, 20, 31, d, d, d, d, d, 26, 22, 201, 41, 22, 16, d, d, 20, d, 21, 25, 18, 261, d, d, d, 194, 72, 21, 18, 157, 25, d, d, d, 29, d, 62, 20, 402, 21, 358, d, d, d, 17, 26, 143, 25, 19, d, d, d, 83, 33, 2300, 21, 18, 19,
103, d, d, 23, 29, 21, 20, 17, 61, d, d, d, 281, 707, 23, 41, 33, 22, 19, d, d, 62, 27, 21,18, 19, 21, d, d, d, 56, 1859, 19, 21, 21, 22, d, d, d, 20, 231, 416, 18, 9651, 208, 3721, d, d, d, 21, 80, 21,156, 22, 1474, d, d, d, 42, 29, 21,
18, 34, 85, d, d, 53, 17, 39, 19, 22, 31, 22, d, d, d, 80, 23, 20, 21, d, 265, d, d, 1328, d, 21, 274, 21, 1201, d, d, d, d, d, 17, 64, 27, 16, d, d, d, 728, 23, 1202, 21, 20}
Flatten@ParallelTable[d /. FindInstance[{9 n == b^3 + c^3 + d^3, b <= c <= d <= 10002}, {b, c, d}, Integers, 1], {n, 5000}]
{2, 3, 3, 3, 4, 3, 7, 4, 3, 6, 6, 1345,  5, 7, 7, 6, 9, 6, 8,  d,  6, 49, 6, 9, 9, 114, 6, 7, 9, 6, 7, 8, 9, 7, 7, 7, 6, 7, 7, 8, 7, 9, 8, 12, 6, 8, 23, 6, 7, 9, 6, 7, 8, 9, 7, 8, 9, 12, 8, 9, 8, 7, 7, 8, 40, 11, 9, 9, 528, 10, 8, 6, 9, 9, 9, 7, 45, 9, 31,
9, 9, 9, 339, 9, 6853, 61, 9, 9, 9, 21, 11, 8, 20, 9, 8, 121, 12, 8, 14, 33, 10, 9, 18, 10, 9, 35, 10, 9, 13, 11, 12, 9, 14, 12, 10, 15, 15, 33, 9, 9, 48, 10, 11, 9, 13, 69, 15, 12, 9, 13, 11, 24, 9, 11, 12, 13, 9, 9, 4928, 12, 21, 17, 19, 12,
9, 24, 11, 11, 12, 11, 11, 11, 12, 14, 11, 13, 14, 11, 9, 14, 12, 9, 13, 13, 9, 50, 14, 12, 15, 17, 12, 11, 205,  14, 23, 9, 13, 12, 12, 15, 14, 13, 15, 12, 12, 9, 16, 41, 15, 57, 12, 12, 12, 120, 12, 27, 21, 12, 12, 12, 25, 33, 13,  3528,
12, 13, 15, 16, 13, 14, 16, 83, 15, 13, 11, 12, 17, 15, 12, 15, 13, d, 14, 14, 16, 19, 15, 15, 11, 13, 14, 18, 2778, 13, 12, 11, 13, 14, 21, 13, 13, 13, 9, 13, 14, 42, 13, 14, 12, 15, 14, 25, 21, d, 13, 12, 25, 13, 11, 637, 13, 14, 15, 15,
12, 21, 14, 13, 13, 15, 15, 14, 12, 21, 34, 12, 13, 1093,  19, 15, 14, 13, 12, 15, 29, 49, 13, 14, 40, 30, 15, 16, d, 15, d, 12, 15, 13, 51, 21, 14, 14, 12, 14, 14, 65, 14, 14, 14, 19, 15, 14, 53, 33, 14, 238, 12, 15, 15, 16, 153, 17, 15,
31, 13, 13, 15, 14, 14, 23, 19, 15, 37, 51, 14, 15, 15, 377, 13, 14, 16, 35, 14, 15, 33, 14, 12, 15, 14, 1136, 15, 20, 17, 15, 186, 105, 14, 43, 69, 12, 15, 15, 45, 52, 65, 20, 15, 15, 15, d, 294, 15, 69, 15, 15, 15, 62, 15, 683, 19, 15,
15, 15, 12, 14, 14, 12, 15, 15, 18, 24, 14, 14, 27, 13, 15, 22, 13, 15, 18, 17, 15, 16, 18, 21, 15, 18, 12, 26, 32, 16, 35, 15, 15, 17, 14, 16, 15, 14, 16, 22, 17, 15, 14, 16, 21, 15, 23, 13, 68, 15, 15, 17, 23, 30, 13, 13, 25, 15, 14, 16,
18, 108, 19, 16, 46, 103, 15, 49, 13, 12, 16, 15, 40, 16, 15, 20, 16, 15, 23, d, 18, 23, 17, 12, 15, 57, 14, 16, 15, 68, 16, 13, 43, 35, 21, 36, 82, 15, 15, d, 40, 14, 21, 20, 15, 15, 16, 17, 363, 18, 17, 13, 19, 39, 14, 14, 16, 19, 15, 18,
22, 17, 14, 25, d, 24, 15, 15, 24, 21, 16, 17, 18, 16, 60, 21, 19, 567, 26, 17, 15, 15, d, 14, 2534, 3639, 22, 16, 15, 24, 15, 7098, 40, 14, 16, 15, 59, 27, 21, 61, 17, 15, 18, 17, 14, 30, 17, 14, 16, 39, 14, 17, 140, 6754, 17, 18, 15, d,
17, 15, 24, 19, 15, 29, 21, 15, 16, 17, 15, 19, 1163, 14, 21, 18, 12, 17, 23, 16, 90, 15, 64, 55, 13,102, 16, 17, 24, 74, 17, 15, 18, 16, 47, 30, 18, 24, 17, 19, 16, 26, 43, 16, 26, 18, 16, 316, 14, 16, 18, 139, 15, 17, 23, 31,17, 18, 33,
15, 15, 18, 20, 15, 18, 20, 17, 16, 29, 168, 14, 21, 62, 15, 15, 18, 2680,  21, d, 783, 16, 18, 18, 19, 39, 18, 215, 16, 15, 18, d, 18, 46, 45, 17, 18, 18, 17, 39, 28, 17, 16, 18, 39, 678, 17, 15, 75, 31, 15, 156, 196, 18, 49, 19, 18, 15,
2069, 21, 15, 15, 17, 19, 20, 16, 21, 18, 15, 122, 26, 23, 18, 19, 54, 43, 19, 18, 20, 5086,  24, 18, 70, 342, 23, 16, 18, 28, 25, 25, 17, 19, 23, 18, 696, 35, 742, 710, 20, 15, 16, 42, 18, 21, 27, 17, 21, 15, 19, 21, 18, 24, 19, 18, 29,
395, 20, 16, 17, 17, 18, 1709, 14, 23, 18, 20, 17, 24, 15, 19, 37, 15, 20, 18, 15, 29, 19, 21,16, 19, 15, 16, 65, 19, 16, 25, 19, 17, 15, 242, 346, 21, 21, 285, 17, 15, d, 17, 33, 23, 19, 27, 18, 18, 27, 16, 21, 19, 17, 21, 30, 17, 15, 16,
17, 20, 16, 18, 27, 28, 39, 19, 22, 69, 18, 33, 18, 23, 20, 20, 17, 18, 76, 24, 21, 17, 20, 18, 36, 21, 19, 57, 453, 19, 16, 36, 40, 1501, d, 27, 19, 16, 15, 20, 25, 18, 20, 19, 18, 23, 76, 18, 16, 83, 18, 16, d, 20, 31, 70, 17, 32, 20, 51,
49, 18, 23, 20, 19, 22, 18, 356, 21, 4060, 2943, 17, 20, 74, 21, 31, 29, 195, 17, 20, 30, 21, 19, 65, 52, 20, 24, 22, 21, 21, 126, 52, 18, 19, 16, 20, 18, 74, 20, 18, 18, 30, 21, 18, 921, 33, 20, 19, 25, 1104, 20, 21, 33, 18, 17, 32, 132,
19, 8087, 20, 19, 46, 22, 19, 21, 21, 20, 17, 17, d, 26, 15, 21, 31, 20, 17, 44, 20, 26, 49, 19, 19, 24, 22, 420, 21, 18, 201, 20, 15, 184, 66, 21, 30, 19, 21, 18, 25, 20, 16, 18, 19, 19, 20, 8765, 38, 17, 18, 187, 26, 22, 359, 21, 23, 50,
19, 20, 20, 25, 21, 21, 25, 66, 20, 17, 16, 80, 143, 21, 17, 24, 22, 36, 19, 24, d, 173, 21, 18, 18, 33, 45, 46, 33, 20, 17, 18, 20, 17, 21, 20, 17, 21, 58, d, 20, 30, 41, 19, 23, 53, 1039, 21, 21, 33, 24, 43, 18, 21, 21, 18, 20, 17, 18, 78,
21, 21, 21, 82, 17, 34, 989, 21, 21, 21, 139, 33, 18, 1233, 21, 19, 23, 773, 18, 18, 22, d, 21, 28, 20, 21, 27, 25, 21, 34, 63, 108, 21, 26, 39, 31, 18, 18, 40, 19, 21, 22, 19, 23, 21, 24, 33, 22, 44, 21, 28, d, 20, 20, 17, 228,  d, 21, 21,
48, 20, 25, 274, 19, 104, 21, 59, 22, 18, 662, 31, 19, 64,  6802, 19, 18, 18, 41, 47, 21, 40, 20, 21, 23,  2075, 21, 105, 24, 19, 18, 1471, 20, 21, 22, 41, 23, 21, 15, 35, 95, 23, 62, 19, 22, 29, 20, 21, 16, 20, 18, 19, 22, 21, 21, 22, 45,
24, 22, 23, 35, 19, 32, 80, 19, 20, 22, 21, 24, 29, 20, 24, 22, 18, 24, 21, 21, 24, 17, 19, 23, 26, 22, 4615, 164, 33, 22, 29, 28, 21, 21,41, 22, 18, 22, 27, 22, 21, 24, 21, 22, 30, 52, 5008, 21, 20, 17, 18, 30, 455, 18, 23, 31, 22, 18, 57,
d,  23,  d,  45, 20, 22, 492, d, 43, 21, 27, 20, 18, 22, 516, 21, 44, 61, 21, 247, 130, 21, 35, 22, 19, 23, 24, 67, 24, 18, 44, 45, 21, 25, 22, 49, 23, 21, 33, 24, 22, 221, 21, 31, 191, 26, 26, 20, ......}