用 1，2，+，×，( )=正整数。

王守恩

northwolves 发表于 2025-5-30 15:51
肯定不是唯一的啦   2+2=2*2

就想减少工作量。
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(1+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),2×2(1+2×2),——2×10,4×5答案相同。
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),——2×12,3×8,4×6答案相同。
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),——2×15,3×10,5×6答案相同。
a(31)=7, 1+(1+2×2)(2+2×2),
a(32)=5, 2×2×2×2×2,

王守恩

northwolves 发表于 2025-5-30 15:51
肯定不是唯一的啦   2+2=2*2

手工心里还是发酥。拿2026去问DeepSeek。这样答复:  1+(1+2×2)(1+2×2)(1+2×2×2)(1+2×2×2)
要计算 a(2026)，即使用数字 1 和 2、运算符 + 和 ×、以及括号表示整数 2026 所需的最小数字数量（运算符和括号不计入数字数量）最终答案为 15。

northwolves

2026=1+45^2，应该就是15

王守恩

王守恩 发表于 2025-5-28 06:31
要不这样想。(2)=(1)+(1)=(1)*(1),   (3)=(1)+(2)=(1)*(2),   (4)=(1)+(3)=(2)+(2)=(1)*(3)=(2)*(2),  .. ...

关键还在5楼！——要不这样想。(2)=(1)+(1)=(1)*(1),   (3)=(1)+(2)=(1)*(2),   (4)=(1)+(3)=(2)+(2)=(1)*(3)=(2)*(2),  ......有规律吗？
(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, 96, 128,
(8) = 43, 46, 47, 53, 55, 57, 58, 61, 62, 63, 67, 69, 70, 73, 74, 75, 76, 78, 81, 82, 84, 85, 88, 90, 97, 98, 99, 100, 102, 104, 108, 112, 120, 129, 130, 132, 136, 144, 160, 192, 256,
(9) = 59, 71, 77, 79, 83, 86, 87, 89, 91, 92, 93, 94, 95, 101, 103, 106, 109, 110, 113, 114, 117, 119, 121, 122, 123, 124, 125, 126, 131, 133, 134, 135, 137, 138, 140, 145, 146, 147, 148, 149, 150, ......, 320, 384, 512,
(10)=107, 115, 118, 127, 139, 141, 142, 143, 149, 151, 152, 153, 154, 155, 156, 157, 158, 159,
(11)=173,
(12)=283,

{1, 3, 5, 7, 11, 19, 23, 43, 59, 107, 173, 283, 383, 719, 1103, 1439, 3019, 4283, 8563, 14207}——我还是搞不出来！

northwolves

1. num = 500; a = Array[20 &, num];
   
2. a[[1]] = a[[2]] = 1;
   
3. Do[Do[s = a[[k]] + a[[n - k]]; If[s < a[[n]], a[[n]] = s];
   
4.    If[Mod[n, k] == 0, s = a[[k]] + a[[n/k]];
   
5.     If[s < a[[n]], a[[n]] = s]], {k, n/2}], {n, 3, num}];
   
6. Table[{k, Select[Range@num, a[[#]] == k &]}, {k, 16}]

复制代码

{{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,{23,29,31,35,37,38,39,41,42,44,45,49,50,51,52,54,56,60,65,66,68,72,80,96,128}},{8,{43,46,47,53,55,57,58,61,62,63,67,69,70,73,74,75,76,78,81,82,84,85,88,90,97,98,99,100,102,104,108,112,120,129,130,132,136,144,160,192,256}},{9,{59,71,77,79,83,86,87,89,91,92,93,94,95,101,103,105,106,109,110,111,113,114,116,117,119,121,122,123,124,125,126,131,133,134,135,137,138,140,145,146,147,148,150,152,153,156,161,162,164,165,168,170,176,180,193,194,195,196,198,200,204,208,216,224,240,257,258,260,264,272,288,320,384}},{10,{107,115,118,127,139,141,142,143,149,151,154,155,157,158,159,163,166,167,169,171,172,174,175,177,178,181,182,183,184,185,186,187,188,189,190,197,199,201,202,205,206,207,209,210,212,217,218,219,220,221,222,225,226,228,231,232,234,238,241,242,243,244,245,246,248,250,252,255,259,261,262,265,266,268,270,273,274,276,280,289,290,291,292,294,296,297,300,304,306,312,321,322,324,325,328,330,336,340,352,360,385,386,387,388,390,392,396,400,408,416,432,448,480}},{11,{173,179,191,203,211,213,214,215,223,227,229,230,233,235,236,237,239,247,249,251,253,254,263,267,269,271,275,277,278,279,281,282,284,285,286,287,293,295,298,299,301,302,303,305,307,308,309,310,313,314,315,316,318,323,326,327,329,331,332,333,334,335,337,338,339,341,342,343,344,345,348,350,351,353,354,356,357,361,362,363,364,365,366,368,369,370,372,374,375,376,378,380,389,391,393,394,397,398,399,401,402,404,405,409,410,411,412,414,417,418,420,424,425,429,433,434,435,436,438,440,441,442,444,449,450,452,455,456,459,462,464,468,476,481,482,483,484,485,486,488,490,492,495,496,500}},{12,{283,311,317,319,346,347,349,355,358,359,367,371,373,377,379,381,382,395,403,406,407,413,415,419,421,422,423,426,427,428,430,431,437,439,443,445,446,447,451,453,454,457,458,460,461,463,465,466,469,470,471,472,474,475,477,478,487,489,491,493,494,497,498}},{13,{383,467,473,479,499}},{14,{}},{15,{}},{16,{}}}

王守恩

northwolves 发表于 2025-5-31 21:59
{{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, ...

太复杂了！仿造不了！只能望洋兴叹！

1. a=Array[9 &, 64]; a[[1]]=a[[2]]=1; Do[Do[s=a[[k]] + a[[n - k]]; If[s < a[[n]], a[[n]]=s]; If[Mod[n, k]==0, s=a[[k]] + a[[n/k]]; If[s < a[[n]], a[[n]]=s]], {k, n/2}], {n, 64}]; Table[a, 1]

复制代码

{{1, 1, 2, 2, 3, 3, 4, 3, 4, 4, 5, 4, 5, 5, 5, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 6, 6, 7, 6, 7, 5, 6, 6, 7, 6, 7, 7, 7, 6, 7, 7, 8, 7, 7, 8, 8, 6, 7, 7, 7, 7, 8, 7, 8, 7, 8, 8, 9, 7, 8, 8, 8, 6}}

王守恩

northwolves 发表于 2025-5-29 21:21
{1, 3, 5, 7, 11, 19, 23, 43, 59, 107, 173, 283, 383, 719, 1103, 1439, 3019, 4283, 8563, 14207, 40013 ...

{1, 3, 5, 7, 11, 19, 23, 43, 59, 107, 173, 283, 383, 719, 1103, 1439, 3019, 4283, 8563, 14207, 40013, 41399, 80437 }

蛮有意思的一串数————没有通项公式才是魅力——你(这是你的)去不去OEIS求助——那是你的事——我是丢了——差不多搞懂了。