从1~100中至少取多少个不同数, 满足a+b=c+d

王守恩

从1~100中至少取多少个不同数, 满足a+b=c+d。a,b,c,d是4个不同数。

王守恩

100太大了, 先从小数试起。

从1~n中取a(n)={A}+{B}={A}+1——{A}尽可能长,不满足a+b=c+d——只要再加{B}中任意1个——就满足a+b=c+d。

a(4)=4, {4,3,2}+{1},
a(5)=5, {5,4,3,1}+{2},
a(6)=5, {6,5,4,2}+{3,1},
a(7)=5, {7,6,5,3}+{4,2,1},
a(8)=6, {8,7,6,4,1}+{5,3,2},
a(9)=6, {9,8,7,5,2}+{6,4,3,1},
a(10)=6, {10,9,8,6,3}+{7,5,4,2,1},
a(11)=6, {11,10,9,7,4}+{8,6,5,3,2,1},
a(12)=6, {12,11,10,8,5}+{9,7,6,4,3,2,1},
a(13)=7, {13,12,11,9,6,1}+{10,8,7,5,4,3,2},
a(14)=7, {14,13,12,10,7,2}+{11,9,8,6,5,4,3,1},
a(15)=7, {15,14,13,11,8,3}+{12,10,9,7,6,5,4,2,1},
a(16)=7, {16,15,14,12,9,4}+{13,11,10,8,7,6,5,3,2,1},
a(17)=7, {17,16,15,13,10,5}+{14,12,11,9,8,7,6,4,3,2,1},
a(18)=7, {18,17,16,14,11,6}+{15,13,12,10,9,8,7,5,4,3,2,1},
a(19)=7, {19,18,17,15,12,7}+{16,14,13,11,10,9,8,6,5,4,3,2,1},
a(20)=7, {20,19,18,16,13,8}+{17,15,14,12,11,10,9,7,6,5,4,3,2,1},
a(21)=8, {21,20,19,17,14,9,1}+{18,16,15,13,12,11,10,8,7,6,5,4,3,2},
a(22)=8, {22,21,20,18,15,10,2}+{19,17,16,14,13,12,11,9,8,7,6,5,4,3,1},
a(23)=8, {23,22,21,19,16,11,3}+{20,18,17,15,14,13,12,10,9,8,7,6,5,4,2,1},
a(24)=8, {24,23,22,20,17,12,4}+{21,19,18,16,15,14,13,11,10,9,8,7,6,5,3,2,1},
a(25)=8, {25,24,23,21,18,13,5}+{22,20,19,17,16,15,14,12,11,10,9,8,7,6,4,3,2,1},
......
后面的还是这个规律吗？譬如：
a(100)=11,{100,99,98,96,93,88,80,67,46,12}+{}
OEIS应该有这串数——就是不知道怎么去找。谢谢各位！