[原创] 用 1，2，+，×，( ) = 正整数

王守恩

用 1，2，+，×，( )。譬如：
a(1)=1, 1,
a(2)=1, 2,
a(3)=2, 1+2,
a(4)=2, 2×2,——能用×的不用+。
a(5)=3, 1+2×2,
a(6)=3, 2+2×2,——能不用( )的不用( )。
a(7)=4, 1+2+2×2,
a(8)=3, 2×2×2,
a(9)=4, 1+2×2×2,
a(10)=4, 2+2×2×2,
a(11)=5, 1+2+2×2×2,
a(12)=4, 2(2+2×2),——能用1个( )的不用2个( )。
a(13)=5, 1+2(2+2×2),
a(14)=5, 2(1+2+2×2),
a(15)=5, (1+2)(1+2×2),
a(16)=4, 2×2×2×2,
a(17)=5, 1+2×2×2×2,
a(18)=5, 2+2×2×2×2,
a(19)=6, 1+2+2×2×2×2,
a(20)=5, 2(2+2×2×2),
a(21)=6, 1+2(2+2×2×2),
a(22)=6, 2(1+2+2×2×2),
a(23)=7, 1+2+2(2+2×2×2),
a(24)=5, 2×2×2(1+2),
a(25)=6, 1+2×2×2(1+2),
a(26)=6, 2+2×2×2(1+2),
a(27)=6, (1+2)(1+2×2×2),
a(28)=6, 2×2(1+2+2×2),
a(29)=7, 1+2×2(1+2+2×2),
a(30)=6, (1+2×2)(2+2×2),
a(31)=7, 1+(1+2×2)(2+2×2),
a(32)=5, 2×2×2×2×2,

特别提一下。
(1) = 1, 2,
(2) = 3, 4,
(3) = 5, 6, 8,
(4) = 7, 9, 10, 12, 16,
(5) = 11, 13, 14, 15, 17, 18, 20, 24, 32,
(6) = 19, 21, 22, 25, 26, 27, 28, 30, 33, 34, 36, 40, 48, 64,
(7) = 23, 29, 31, 35, 37, 38, 39, 41, 42, 44, 45, 49, 50, 51, 52, 54, 56, 60, 65, 66, 68, 72, 80,
(8) = 43, 46, 47, 53, 55, 57, 58, 61, 62, 63, 67, 69, 70, 73, 74, 75, 76, 77, 78, 81, 62, 84, 85, 66, 90,
(9) = 59, 71, 79, 83, 86, 87, 89,
(10)=107,
(11)=173,
(12)=283,

再特别提一下。
a(1)=1, 1,
a(2)=3, 1+2,
a(3)=5, 1+2×2,
a(4)=7, 1+2+2×2,
a(5)=11, 1+2+2×2×2,
a(6)=19, 1+2+2×2×2×2,
a(7)=23, 1+2+2(2+2×2×2),
a(8)=43, 1+2+2×2(2+2×2×2),
a(9)=59, 1+2+2×2(2+2(2+2×2)),
a(10)=107, 1+2+2×2(2+2×2(2+2×2)),
a(11)=173, 1+2+2(1+2×2)(1+2×2×2×2),
a(12)=283, 1+2+2×2(2+2(2+2×2×2×2×2)),
a(13)=383, 1+2+2×2(1+2×2)(1+(2+2×2×2×2)),
a(14)=719, 1+2(2+(1+2)(1+2+2×2)(1+2×2×2×2)),
a(15)=1103, 1+2+2(2+2(2+2×2×2(2+2×2×2×2×2))),
a(16)=1439, 1+2+2×2(2+(1+2)(1+2+2×2)(1+2×2×2×2)),
a(17)=3019, 1+2+2×2(2+2×2×2×2(2+(1+2)(1+2)(1+2×2))),
a(18)=4283, 1+2+2×2(2+2(2+2(2+2×2(2+2×2×2×2×2×2)))),
a(19)=8563, 1+2+2×2×2(2+2(2+2(2+2×2(2+2×2×2×2×2×2)))),
a(20)=14207, 1+2+2×2(2+(1+2(2+2×2))(1+2×2×2(2+2×2×2×2×2))),
a(21)=40013, 1+2+2(1+2×2)(1+2×2×2×2×2(1+2×2)(1+2×2(2+2×2))),
a(22)=41399, 1+2+2(2+2×2×2(2+(1+2×2)(1+2(2+2×2×2×2×2×2×2×2)))),
a(23)=80437, 1+2+2(1+2(1+2)(1+2)(1+2×2×2×2))(1+(2+2×2×2×2×2×2×2)),

漂亮！让您遐想！！—— 1与2的简单组合——OEIS也没有！！！——谢谢 northwolves！