求{1, 2, ..., 100}没有等和对的最大子集

王守恩

northwolves 发表于 2025-7-21 23:37
Table 改为 Do 即可：

搬运一下——用了4个小时。
Do[K={0, a1, a2, a3, a4, a5, a6, a7, a8, 45};S=Total/@Subsets[K,{2}];If[Length[S]==Length[Union[S]],Print[{Length[S],K}]],{a1, 37},{a2, a1+1, 38},{a3, a2+1, 39},{a4, a3+1, 40},{a5, a4+1, 41},{a6, a5+1, 42},{a7, a6+1, 43},{a8, a7+1, 44}]
{45,{0,1,7,10,13,21,26,41,43,45}}
{45,{0,2,4,19,24,32,35,38,44,45}}

王守恩

A345731——Additive bases: a(n) is the least integer such that there is an n-element set of integers between 0 and a(n), the sums of pairs (of distinct elements) of which are distinct.
A345731——1, 2, 4, 7, 12, 18, 24, 34, 45, 57, 71, 86, 105, 126, 150, 171,——Table of n, a(n) for n=2..17.——{0, 1, 2, 3, ..., a(n)}没有等和对的最大子集。

a(1)=0,  0,
a(2)=1,  0, 1,
a(3)=2,  0, 1, 2,
a(4)=4,  0, 2, 3, 4,
a(5)=7,  0, 3, 5, 6, 7,
a(6)=12,  0, 1, 2, 6, 9, 12,
a(7)=18,  0, 1, 2, 4, 8, 13, 18,
a(8)=24,  0, 1, 2, 4, 8, 14, 19, 24,
a(9)=34,  0, 1, 2, 4, 8, 15, 24, 29, 34,
a(10)=45,  0, 1, 7, 10, 13, 21, 26, 41, 43, 45,
a(11)=57,  0, 1, 5, 9, 17, 31, 33, 44, 51, 54, 57,
a(12)=71,  0, 1, 2,  7, 12 22, 37, 40, 54, 63, 67, 71,
a(13)=86,  0, 1, 11, 17, 21, 34, 42, 57, 60, 72, 79, 84, 86,——72,79,86可以成等差数列。
a(14)=105,  0, 1, 6, 14, 27, 44 54 66, 69, 85, 94, 101, 103, 105,
a(15)=126,  0, 8, 13, 16, 19, 31, 46, 76, 83, 90, 100, 104, 124, 125, 126,
a(16)=148,  0, 3, 5, 6, 32, 49, 59, 68, 93, 106, 118, 126, 130, 134, 141, 148,
a(17)=171,