有这样一串数(OEIS找不到)

northwolves · 发表于 2024-5-13 13:27:53

n=5

51975 {1,3,21,25,33} {5,7,9,11,15}
51975 {1,5,15,21,33} {3,7,9,11,25}
51975 {1,7,9,25,33} {3,5,11,15,21}
51975 {1,9,11,21,25} {3,5,7,15,33}

northwolves · 发表于 2024-5-13 13:32:36

n=6

1216215 {1,3,15,21,33,39} {5,7,9,11,13,27}
1216215 {1,5,7,27,33,39} {3,9,11,13,15,21}
1216215 {1,5,9,21,33,39} {3,7,11,13,15,27}
1216215 {1,5,11,21,27,39} {3,7,9,13,15,33}
1216215 {1,5,13,21,27,33} {3,7,9,11,15,39}
1216215 {1,7,9,15,33,39} {3,5,11,13,21,27}
1216215 {1,7,11,15,27,39} {3,5,9,13,21,33}
1216215 {1,7,13,15,27,33} {3,5,9,11,21,39}
1216215 {1,9,11,15,21,39} {3,5,7,13,27,33}
1216215 {1,9,13,15,21,33} {3,5,7,11,27,39}
1216215 {1,11,13,15,21,27} {3,5,7,9,33,39}

northwolves · 发表于 2024-5-13 13:37:07

n=7

42567525 {1,3,9,25,33,39,49} {5,7,11,13,15,21,27}
42567525 {1,3,11,25,27,39,49} {5,7,9,13,15,21,33}
42567525 {1,3,13,25,27,33,49} {5,7,9,11,15,21,39}
42567525 {1,5,9,15,33,39,49} {3,7,11,13,21,25,27}
42567525 {1,5,11,15,27,39,49} {3,7,9,13,21,25,33}
42567525 {1,5,13,15,27,33,49} {3,7,9,11,21,25,39}
42567525 {1,7,9,21,25,33,39} {3,5,11,13,15,27,49}
42567525 {1,7,11,21,25,27,39} {3,5,9,13,15,33,49}
42567525 {1,7,13,21,25,27,33} {3,5,9,11,15,39,49}
42567525 {1,9,11,13,25,27,49} {3,5,7,15,21,33,39}

mathe · 发表于 2024-5-13 14:54:52

我们已经得出使用2N个不同的正整数得出的最小平方数的算数平方根，然后每个平方数可能会有多种正整数的组合选择。
而对于每个2N个正整数组合，划分成两组的方案也可能会有多组，我们可以计算一下它们的方案数目如下(A372794) , 使用动态规划的C++代码速度还不错，现在的主要限制在内存了:

N=2
6<1>
{ 1 2 3 6 }<1>

N=3
36<1>
{ 1 2 3 4 6 9 }<1>

N=4
240<1>
{ 1 2 3 4 5 6 8 10 }<3>

N=5
2520<1>
{ 1 2 3 4 5 6 7 9 10 14 }<4>

N=6
30240<3>
{ 1 2 3 4 5 6 7 8 9 12 14 15 }<10>
{ 1 2 3 4 5 6 7 8 9 10 14 18 }<11>
{ 1 2 3 4 5 6 7 8 9 10 12 21 }<10>

N=7
443520<1>
{ 1 2 3 4 5 6 7 8 9 10 11 14 16 22 }<15>

N=8
6652800<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 14 15 20 22 }<55>

N=9
133056000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 20 22 25 }<110>

N=10
2075673600<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 20 22 26 }<280>

N=11
58118860800<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 20 21 22 24 26 28 }<797>

N=12
1270312243200<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 20 22 24 26 27 34 }<1419>

N=13
29640619008000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 20 21 22 24 25 26 28 34 }<3557>

N=14
844757641728000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 25 26 27 28 34 38 }<5647>

N=15
25342729251840000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 24 25 26 27 30 34 35 38 }<19559>

N=16
810967336058880000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 24 25 26 27 28 30 32 34 38 40 }<59708>

N=17
27978373094031360000<3>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 30 32 34 35 36 38 46 }<115592>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 30 34 36 38 40 46 }<129320>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 30 32 34 38 45 46 }<115814>

N=18
1077167364120207360000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 30 33 34 35 38 42 44 46 }<346487>

N=19
43086694564808294400000<2>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 30 32 33 34 35 38 42 44 46 50 }<983805>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 30 32 33 34 35 38 40 42 46 55 }<1034227>

N=20
1499416970855328645120000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 33 34 35 36 38 42 44 46 58 }<2106172>

N=21
74970848542766432256000000<2>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 33 34 35 38 40 42 44 45 46 50 58 }<6618558>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 33 34 35 36 38 40 42 46 50 55 58 }<6609936>

N=22
2788915565790911279923200000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 38 40 42 44 45 46 58 62 }<13994982>

N=23
140345428472058761183232000000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 33 34 35 36 38 39 40 42 44 45 46 48 50 52 58 }<65426469>

N=24
6090991595687350235352268800000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 38 39 40 42 44 45 46 48 49 52 58 62 }<110980446>

N=25
321952412914902798154334208000000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 42 44 45 46 48 50 52 58 62 74 }<257148638>

N=26
18029335123234556696642715648000000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 42 44 45 46 48 49 50 52 58 62 64 74 }<660593345>

N=27
1103395309541954869834534197657600000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 42 44 45 46 48 49 51 52 54 58 62 64 68 74 }<1966842579>

N=28
56549009614025187079019877629952000000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 44 45 46 48 49 50 51 52 54 58 62 68 74 82 }<3909078573>

N=29
3641204521488451070453962852270080000000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 42 44 45 46 48 49 50 51 52 54 55 58 60 62 64 66 68 74 }<20820932559>

N=30
204255022725858975729419797999386624000000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 48 49 50 51 52 54 56 58 62 63 68 74 82 86 }<26864715089>

N=31
12540308372006225486643448063218155520000000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 44 45 46 48 49 50 51 52 54 55 56 58 60 62 63 64 66 68 74 82 }<144689720443>

N=32
808849889994401543888502400077571031040000000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 48 49 50 51 52 54 55 56 58 60 62 63 66 68 72 74 82 86 }<307476230099>

N=33
50687926439649163417012817071527784611840000000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 54 55 56 58 60 62 63 64 66 68 74 82 86 94 }<571509614773>

N=34
3611514758825002893462163216346354653593600000000<1>
{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 54 55 56 57 58 60 62 63 66 68 74 75 76 82 86 94 }<1695094248112>

王守恩 · 发表于 2024-5-13 16:24:06

本帖最后由王守恩于 2024-5-13 18:49 编辑

N=02, =$\frac{ 2* 3 }{ 1* 6 }$

N=03, $\frac{ 2* 3 }{ 1* 6 }*\frac{3*2}{1}=\frac{ 2* 3* 6 }{ 1* 4* 9 }$

N=04, $\frac{ 2* 3* 6 }{ 1* 4* 9 }*\frac{5*4}{3}=\frac{ 2* 4* 5* 6 }{ 1* 3* 8* 10 }$
,
N=05, $\frac{ 2* 4* 5* 6 }{ 1* 3 *8* 10 }*\frac{7*3}{2}=\frac{ 3* 4* 5* 6* 7 }{ 1* 2* 9* 10* 14 }$

N=06, $\frac{ 3* 4* 5* 6* 7 }{ 1* 2* 9* 10* 14 }*\frac{4*3}{1}=\frac{ 2* 5* 6* 7* 8* 9 }{ 1* 3* 4* 12* 14* 15 }=\frac{ 2* 5* 6* 7* 8* 9 }{ 1* 3* 4* 10* 14* 18 }=\frac{ 2* 5* 6* 7* 8* 9 }{ 1* 3* 4* 10* 12* 21 }$

N=07, $\frac{ 2* 5* 6* 7* 8* 9 }{ 1* 3* 4* 12* 14* 15 }*\frac{11*4}{3}=\frac{ 3 *4* 5* 6* 7* 8* 22 }{ 1* 2* 9* 10* 11* 14* 16 }$

N=08, $\frac{ 3 *4* 5* 6* 7* 8* 22 }{ 1* 2* 9* 10* 11* 14* 16 }*\frac{5*3}{1}=\frac{ 4 *5* 6* 7* 8* 9* 10* 11 }{ 1 *2 *3* 12* 14* 15* 20* 22 }$

N=09, $\frac{ 4 *5* 6* 7* 8* 9* 10* 11 }{ 1 *2 *3* 12* 14* 15* 20* 22 }*\frac{5*4}{1}=\frac{ 2*5* 7* 8* 9* 10* 11* 12* 20 }{ 1* 3* 4* 6* 14* 15* 16* 22* 25 }$

N=10, $\frac{ 2*5* 7* 8* 9* 10* 11* 12* 20 }{ 1* 3* 4* 6* 14* 15* 16* 22* 25 }*\frac{13*3*2}{5}=\frac{ 2 *6* 7* 8* 9* 10* 11* 12* 13* 20 }{ 1 *3 *4 *5* 14* 15* 16* 18* 22* 26 }$

N=11, $\frac{ 2 *6* 7* 8* 9* 10* 11* 12* 13* 20 }{ 1 *3 *4 *5* 14* 15* 16* 18* 22* 26 }*\frac{7*4}{1}=\frac{ 2 *7* 8* 9* 10* 11* 12* 13* 14* 15* 16 }{ 1* 3* 4* 5* 6* 20* 21* 22* 24* 26* 28 }$

N=12, $\frac{ 2 *7* 8* 9* 10* 11* 12* 13* 14* 15* 16 }{ 1* 3* 4* 5* 6* 20* 21* 22* 24* 26* 28 }*\frac{17*9}{7}=\frac{ 2 *3* 4* 5* 6* 7* 20* 22* 24* 26* 27* 34 }{ 1* 8* 9* 10* 11* 12* 13* 14* 15* 16* 17* 18 }$

N=13, $\frac{ 2 *3* 4* 5* 6* 7* 20* 22* 24* 26* 27* 34 }{ 1* 8* 9* 10* 11* 12* 13* 14* 15* 16* 17* 18 }*\frac{7*5*2}{3}=\frac{ 3* 7* 8* 9* 10* 11* 12* 13* 14* 15* 16* 17* 20 }{ 1* 2* 4* 5* 6* 18* 21* 22* 24* 25* 26* 28* 34 }$

N=14, $\frac{ 3* 7* 8* 9* 10* 11* 12* 13* 14* 15* 16* 17* 20 }{ 1* 2* 4* 5* 6* 18* 21* 22* 24* 25* 26* 28* 34 }*\frac{19*3}{2}=\frac{ 2* 7* 9* 10* 11* 12* 13* 14* 15* 16* 17* 18* 19* 20 }{ 1* 3* 4* 5* 6* 8* 21* 22* 25* 26* 27* 28* 34* 38 }$

N=15, $\frac{ 2* 7* 9* 10* 11* 12* 13* 14* 15* 16* 17* 18* 19* 20 }{ 1* 3* 4* 5* 6* 8* 21* 22* 25* 26* 27* 28* 34* 38 }*\frac{5*3*2}{1}=\frac{ 4* 5* 9* 10* 11* 12* 13* 14* 15* 16* 17* 18* 19* 20* 21 }{ 1* 2* 3* 6* 7* 8* 22* 24* 25* 26* 27* 30*34*35*38 }$

N=16, $\frac{ 4* 5* 9* 10* 11* 12* 13* 14* 15* 16* 17* 18* 19* 20* 21 }{ 1* 2* 3* 6* 7* 8* 22* 24* 25* 26* 27* 30*34*35*38 }*\frac{32}{1}=\frac{ 5* 6* 8* 10* 11* 12* 13* 14* 15* 16* 17* 18* 19* 20* 21* 24 }{ 1* 2* 3* 4* 7* 9* 22* 25* 26* 27* 28* 30* 32* 34* 38* 40 }$

N=17,$\frac{ 5* 6* 8* 10* 11* 12* 13* 14* 15* 16* 17* 18* 19* 20* 21* 24 }{ 1* 2* 3* 4* 7* 9* 22* 25* 26* 27* 28* 30* 32* 34* 38* 40 }$*$\frac{23*3}{2}$=$\frac{ 4 *5 *9 *10* 12* 13* 14* 15* 16* 17* 18* 19* 20* 21* 22* 23* 24 }{ 1* 2* 3* 6* 7* 8* 11* 25* 26* 27* 30* 32* 34* 35* 36* 38* 46 }$=$\frac{ 4 *5 *9 *10* 12* 13* 14* 15* 16* 17* 18* 19* 20* 21* 22* 23* 24 }{ 1* 2* 3* 6* 7* 8* 11* 25* 26* 27* 28* 30* 34* 36* 38*40* 46 }$=$\frac{ 4 *5 *9 *10* 12* 13* 14* 15* 16* 17* 18* 19* 20* 21* 22* 23* 24 }{ 1* 2* 3* 6* 7* 8* 11* 25* 26* 27*28*30*32*34*38* 45*46 }$

N=18, $\frac{ 4 *5 *9 *10* 12* 13* 14* 15* 16* 17* 18* 19* 20* 21* 22* 23* 24 }{ 1* 2* 3* 6* 7* 8* 11* 25* 26* 27* 30* 32* 34* 35* 36* 38* 46 }*\frac{11*7}{2}=\frac{ 2* 3* 4* 5* 6* 7* 8* 10* 26* 27* 30* 33* 34* 35* 38* 42* 44* 46 }{1* 9* 11* 12* 13* 14* 15* 16* 17* 18* 19* 20* 21* 22* 23* 24* 25* 28 }$

N=19, $\frac{ 2* 3* 4* 5* 6* 7* 8* 10* 26* 27* 30* 33* 34* 35* 38* 42* 44* 46 }{1* 9* 11* 12* 13* 14* 15* 16* 17* 18* 19* 20* 21* 22* 23* 24* 25* 28 }*\frac{5*8}{1}=\frac{ 4* 9* 10* 11* 12* 13* 14* 15* 16* 17* 18* 19* 20* 21* 22* 23* 24* 25* 28 }{ 1 *2 *3 *5 *6 *7* 8* 26* 27* 30* 32* 33* 34* 35* 38* 42* 44* 46* 50 }=\frac{ 4* 9* 10* 11* 12* 13* 14* 15* 16* 17* 18* 19* 20* 21* 22* 23* 24* 25* 28 }{ 1 *2 *3 *5 *6 *7* 8* 26* 27* 30* 32* 33* 34* 35* 38* 40* 42* 46* 55 }$

northwolves · 发表于 2024-5-13 17:43:57

n=8

1178512335 {1,3,5,21,33,39,51,57} {7,9,11,13,15,17,19,27}
1178512335 {1,3,7,15,33,39,51,57} {5,9,11,13,17,19,21,27}
1178512335 {1,3,11,15,21,39,51,57} {5,7,9,13,17,19,27,33}
1178512335 {1,3,13,15,21,33,51,57} {5,7,9,11,17,19,27,39}
1178512335 {1,3,15,17,21,33,39,57} {5,7,9,11,13,19,27,51}
1178512335 {1,3,15,19,21,33,39,51} {5,7,9,11,13,17,27,57}
1178512335 {1,5,7,9,33,39,51,57} {3,11,13,15,17,19,21,27}
1178512335 {1,5,7,11,27,39,51,57} {3,9,13,15,17,19,21,33}
1178512335 {1,5,7,13,27,33,51,57} {3,9,11,15,17,19,21,39}
1178512335 {1,5,7,17,27,33,39,57} {3,9,11,13,15,19,21,51}
1178512335 {1,5,7,19,27,33,39,51} {3,9,11,13,15,17,21,57}
1178512335 {1,5,9,11,21,39,51,57} {3,7,13,15,17,19,27,33}
1178512335 {1,5,9,13,21,33,51,57} {3,7,11,15,17,19,27,39}
1178512335 {1,5,9,17,21,33,39,57} {3,7,11,13,15,19,27,51}
1178512335 {1,5,9,19,21,33,39,51} {3,7,11,13,15,17,27,57}
1178512335 {1,5,11,13,21,27,51,57} {3,7,9,15,17,19,33,39}
1178512335 {1,5,11,17,21,27,39,57} {3,7,9,13,15,19,33,51}
1178512335 {1,5,11,19,21,27,39,51} {3,7,9,13,15,17,33,57}
1178512335 {1,5,13,17,21,27,33,57} {3,7,9,11,15,19,39,51}
1178512335 {1,5,13,19,21,27,33,51} {3,7,9,11,15,17,39,57}
1178512335 {1,5,17,19,21,27,33,39} {3,7,9,11,13,15,51,57}
1178512335 {1,7,9,11,15,39,51,57} {3,5,13,17,19,21,27,33}
1178512335 {1,7,9,13,15,33,51,57} {3,5,11,17,19,21,27,39}
1178512335 {1,7,9,15,17,33,39,57} {3,5,11,13,19,21,27,51}
1178512335 {1,7,9,15,19,33,39,51} {3,5,11,13,17,21,27,57}
1178512335 {1,7,11,13,15,27,51,57} {3,5,9,17,19,21,33,39}
1178512335 {1,7,11,15,17,27,39,57} {3,5,9,13,19,21,33,51}
1178512335 {1,7,11,15,19,27,39,51} {3,5,9,13,17,21,33,57}
1178512335 {1,7,13,15,17,27,33,57} {3,5,9,11,19,21,39,51}
1178512335 {1,7,13,15,19,27,33,51} {3,5,9,11,17,21,39,57}
1178512335 {1,7,15,17,19,27,33,39} {3,5,9,11,13,21,51,57}
1178512335 {1,9,11,13,15,21,51,57} {3,5,7,17,19,27,33,39}
1178512335 {1,9,11,15,17,21,39,57} {3,5,7,13,19,27,33,51}
1178512335 {1,9,11,15,19,21,39,51} {3,5,7,13,17,27,33,57}
1178512335 {1,9,13,15,17,21,33,57} {3,5,7,11,19,27,39,51}
1178512335 {1,9,13,15,19,21,33,51} {3,5,7,11,17,27,39,57}
1178512335 {1,9,15,17,19,21,33,39} {3,5,7,11,13,27,51,57}
1178512335 {1,11,13,15,17,21,27,57} {3,5,7,9,19,33,39,51}
1178512335 {1,11,13,15,19,21,27,51} {3,5,7,9,17,33,39,57}
1178512335 {1,11,15,17,19,21,27,39} {3,5,7,9,13,33,51,57}
1178512335 {1,13,15,17,19,21,27,33} {3,5,7,9,11,39,51,57}

northwolves · 发表于 2024-5-13 17:44:32

n=9

41247931725 {1,3,5,15,33,39,49,51,57} {7,9,11,13,17,19,21,25,27}
41247931725 {1,3,7,21,25,33,39,51,57} {5,9,11,13,15,17,19,27,49}
41247931725 {1,3,9,11,25,39,49,51,57} {5,7,13,15,17,19,21,27,33}
41247931725 {1,3,9,13,25,33,49,51,57} {5,7,11,15,17,19,21,27,39}
41247931725 {1,3,9,17,25,33,39,49,57} {5,7,11,13,15,19,21,27,51}
41247931725 {1,3,9,19,25,33,39,49,51} {5,7,11,13,15,17,21,27,57}
41247931725 {1,3,11,13,25,27,49,51,57} {5,7,9,15,17,19,21,33,39}
41247931725 {1,3,11,17,25,27,39,49,57} {5,7,9,13,15,19,21,33,51}
41247931725 {1,3,11,19,25,27,39,49,51} {5,7,9,13,15,17,21,33,57}
41247931725 {1,3,13,17,25,27,33,49,57} {5,7,9,11,15,19,21,39,51}
41247931725 {1,3,13,19,25,27,33,49,51} {5,7,9,11,15,17,21,39,57}
41247931725 {1,3,17,19,25,27,33,39,49} {5,7,9,11,13,15,21,51,57}
41247931725 {1,5,7,15,21,33,39,51,57} {3,9,11,13,17,19,25,27,49}
41247931725 {1,5,9,11,15,39,49,51,57} {3,7,13,17,19,21,25,27,33}
41247931725 {1,5,9,13,15,33,49,51,57} {3,7,11,17,19,21,25,27,39}
41247931725 {1,5,9,15,17,33,39,49,57} {3,7,11,13,19,21,25,27,51}
41247931725 {1,5,9,15,19,33,39,49,51} {3,7,11,13,17,21,25,27,57}
41247931725 {1,5,11,13,15,27,49,51,57} {3,7,9,17,19,21,25,33,39}
41247931725 {1,5,11,15,17,27,39,49,57} {3,7,9,13,19,21,25,33,51}
41247931725 {1,5,11,15,19,27,39,49,51} {3,7,9,13,17,21,25,33,57}
41247931725 {1,5,13,15,17,27,33,49,57} {3,7,9,11,19,21,25,39,51}
41247931725 {1,5,13,15,19,27,33,49,51} {3,7,9,11,17,21,25,39,57}
41247931725 {1,5,15,17,19,27,33,39,49} {3,7,9,11,13,21,25,51,57}
41247931725 {1,7,9,11,21,25,39,51,57} {3,5,13,15,17,19,27,33,49}
41247931725 {1,7,9,13,21,25,33,51,57} {3,5,11,15,17,19,27,39,49}
41247931725 {1,7,9,17,21,25,33,39,57} {3,5,11,13,15,19,27,49,51}
41247931725 {1,7,9,19,21,25,33,39,51} {3,5,11,13,15,17,27,49,57}
41247931725 {1,7,11,13,21,25,27,51,57} {3,5,9,15,17,19,33,39,49}
41247931725 {1,7,11,17,21,25,27,39,57} {3,5,9,13,15,19,33,49,51}
41247931725 {1,7,11,19,21,25,27,39,51} {3,5,9,13,15,17,33,49,57}
41247931725 {1,7,13,17,21,25,27,33,57} {3,5,9,11,15,19,39,49,51}
41247931725 {1,7,13,19,21,25,27,33,51} {3,5,9,11,15,17,39,49,57}
41247931725 {1,7,17,19,21,25,27,33,39} {3,5,9,11,13,15,49,51,57}
41247931725 {1,9,11,13,17,25,27,49,57} {3,5,7,15,19,21,33,39,51}
41247931725 {1,9,11,13,19,25,27,49,51} {3,5,7,15,17,21,33,39,57}
41247931725 {1,9,11,17,19,25,27,39,49} {3,5,7,13,15,21,33,51,57}
41247931725 {1,9,13,17,19,25,27,33,49} {3,5,7,11,15,21,39,51,57}

northwolves · 发表于 2024-5-13 17:45:21

n=10

2032933777875 {1,3,5,7,33,45,51,57,65,69} {9,11,13,15,17,19,21,23,25,27}
2032933777875 {1,3,5,11,21,45,51,57,65,69} {7,9,13,15,17,19,23,25,27,33}
2032933777875 {1,3,5,15,21,33,51,57,65,69} {7,9,11,13,17,19,23,25,27,45}
2032933777875 {1,3,5,17,21,33,45,57,65,69} {7,9,11,13,15,19,23,25,27,51}
2032933777875 {1,3,5,19,21,33,45,51,65,69} {7,9,11,13,15,17,23,25,27,57}
2032933777875 {1,3,5,21,23,33,45,51,57,65} {7,9,11,13,15,17,19,25,27,69}
2032933777875 {1,3,7,9,25,33,51,57,65,69} {5,11,13,15,17,19,21,23,27,45}
2032933777875 {1,3,7,11,15,45,51,57,65,69} {5,9,13,17,19,21,23,25,27,33}
2032933777875 {1,3,7,11,25,27,51,57,65,69} {5,9,13,15,17,19,21,23,33,45}
2032933777875 {1,3,7,13,25,33,45,51,57,69} {5,9,11,15,17,19,21,23,27,65}
2032933777875 {1,3,7,15,17,33,45,57,65,69} {5,9,11,13,19,21,23,25,27,51}
2032933777875 {1,3,7,15,19,33,45,51,65,69} {5,9,11,13,17,21,23,25,27,57}
2032933777875 {1,3,7,15,23,33,45,51,57,65} {5,9,11,13,17,19,21,25,27,69}
2032933777875 {1,3,7,17,25,27,33,57,65,69} {5,9,11,13,15,19,21,23,45,51}
2032933777875 {1,3,7,19,25,27,33,51,65,69} {5,9,11,13,15,17,21,23,45,57}
2032933777875 {1,3,7,23,25,27,33,51,57,65} {5,9,11,13,15,17,19,21,45,69}
2032933777875 {1,3,9,11,21,25,51,57,65,69} {5,7,13,15,17,19,23,27,33,45}
2032933777875 {1,3,9,17,21,25,33,57,65,69} {5,7,11,13,15,19,23,27,45,51}
2032933777875 {1,3,9,19,21,25,33,51,65,69} {5,7,11,13,15,17,23,27,45,57}
2032933777875 {1,3,9,21,23,25,33,51,57,65} {5,7,11,13,15,17,19,27,45,69}
2032933777875 {1,3,11,13,21,25,45,51,57,69} {5,7,9,15,17,19,23,27,33,65}
2032933777875 {1,3,11,15,17,21,45,57,65,69} {5,7,9,13,19,23,25,27,33,51}
2032933777875 {1,3,11,15,19,21,45,51,65,69} {5,7,9,13,17,23,25,27,33,57}
2032933777875 {1,3,11,15,21,23,45,51,57,65} {5,7,9,13,17,19,25,27,33,69}
2032933777875 {1,3,11,17,21,25,27,57,65,69} {5,7,9,13,15,19,23,33,45,51}
2032933777875 {1,3,11,19,21,25,27,51,65,69} {5,7,9,13,15,17,23,33,45,57}
2032933777875 {1,3,11,21,23,25,27,51,57,65} {5,7,9,13,15,17,19,33,45,69}
2032933777875 {1,3,13,15,21,25,33,51,57,69} {5,7,9,11,17,19,23,27,45,65}
2032933777875 {1,3,13,17,21,25,33,45,57,69} {5,7,9,11,15,19,23,27,51,65}
2032933777875 {1,3,13,19,21,25,33,45,51,69} {5,7,9,11,15,17,23,27,57,65}
2032933777875 {1,3,13,21,23,25,33,45,51,57} {5,7,9,11,15,17,19,27,65,69}
2032933777875 {1,3,15,17,19,21,33,45,65,69} {5,7,9,11,13,23,25,27,51,57}
2032933777875 {1,3,15,17,21,23,33,45,57,65} {5,7,9,11,13,19,25,27,51,69}
2032933777875 {1,3,15,19,21,23,33,45,51,65} {5,7,9,11,13,17,25,27,57,69}
2032933777875 {1,3,17,19,21,25,27,33,65,69} {5,7,9,11,13,15,23,45,51,57}
2032933777875 {1,3,17,21,23,25,27,33,57,65} {5,7,9,11,13,15,19,45,51,69}
2032933777875 {1,3,19,21,23,25,27,33,51,65} {5,7,9,11,13,15,17,45,57,69}
2032933777875 {1,5,7,9,11,45,51,57,65,69} {3,13,15,17,19,21,23,25,27,33}
2032933777875 {1,5,7,9,15,33,51,57,65,69} {3,11,13,17,19,21,23,25,27,45}
2032933777875 {1,5,7,9,17,33,45,57,65,69} {3,11,13,15,19,21,23,25,27,51}
2032933777875 {1,5,7,9,19,33,45,51,65,69} {3,11,13,15,17,21,23,25,27,57}
2032933777875 {1,5,7,9,23,33,45,51,57,65} {3,11,13,15,17,19,21,25,27,69}
2032933777875 {1,5,7,11,15,27,51,57,65,69} {3,9,13,17,19,21,23,25,33,45}
2032933777875 {1,5,7,11,17,27,45,57,65,69} {3,9,13,15,19,21,23,25,33,51}
2032933777875 {1,5,7,11,19,27,45,51,65,69} {3,9,13,15,17,21,23,25,33,57}
2032933777875 {1,5,7,11,23,27,45,51,57,65} {3,9,13,15,17,19,21,25,33,69}
2032933777875 {1,5,7,13,15,33,45,51,57,69} {3,9,11,17,19,21,23,25,27,65}
2032933777875 {1,5,7,13,25,27,33,51,57,69} {3,9,11,15,17,19,21,23,45,65}
2032933777875 {1,5,7,15,17,27,33,57,65,69} {3,9,11,13,19,21,23,25,45,51}
2032933777875 {1,5,7,15,19,27,33,51,65,69} {3,9,11,13,17,21,23,25,45,57}
2032933777875 {1,5,7,15,23,27,33,51,57,65} {3,9,11,13,17,19,21,25,45,69}
2032933777875 {1,5,7,17,19,27,33,45,65,69} {3,9,11,13,15,21,23,25,51,57}
2032933777875 {1,5,7,17,23,27,33,45,57,65} {3,9,11,13,15,19,21,25,51,69}
2032933777875 {1,5,7,19,23,27,33,45,51,65} {3,9,11,13,15,17,21,25,57,69}
2032933777875 {1,5,9,11,15,21,51,57,65,69} {3,7,13,17,19,23,25,27,33,45}
2032933777875 {1,5,9,11,17,21,45,57,65,69} {3,7,13,15,19,23,25,27,33,51}
2032933777875 {1,5,9,11,19,21,45,51,65,69} {3,7,13,15,17,23,25,27,33,57}
2032933777875 {1,5,9,11,21,23,45,51,57,65} {3,7,13,15,17,19,25,27,33,69}
2032933777875 {1,5,9,13,21,25,33,51,57,69} {3,7,11,15,17,19,23,27,45,65}
2032933777875 {1,5,9,15,17,21,33,57,65,69} {3,7,11,13,19,23,25,27,45,51}
2032933777875 {1,5,9,15,19,21,33,51,65,69} {3,7,11,13,17,23,25,27,45,57}
2032933777875 {1,5,9,15,21,23,33,51,57,65} {3,7,11,13,17,19,25,27,45,69}
2032933777875 {1,5,9,17,19,21,33,45,65,69} {3,7,11,13,15,23,25,27,51,57}
2032933777875 {1,5,9,17,21,23,33,45,57,65} {3,7,11,13,15,19,25,27,51,69}
2032933777875 {1,5,9,19,21,23,33,45,51,65} {3,7,11,13,15,17,25,27,57,69}
2032933777875 {1,5,11,13,15,21,45,51,57,69} {3,7,9,17,19,23,25,27,33,65}
2032933777875 {1,5,11,13,21,25,27,51,57,69} {3,7,9,15,17,19,23,33,45,65}
2032933777875 {1,5,11,15,17,21,27,57,65,69} {3,7,9,13,19,23,25,33,45,51}
2032933777875 {1,5,11,15,19,21,27,51,65,69} {3,7,9,13,17,23,25,33,45,57}
2032933777875 {1,5,11,15,21,23,27,51,57,65} {3,7,9,13,17,19,25,33,45,69}
2032933777875 {1,5,11,17,19,21,27,45,65,69} {3,7,9,13,15,23,25,33,51,57}
2032933777875 {1,5,11,17,21,23,27,45,57,65} {3,7,9,13,15,19,25,33,51,69}
2032933777875 {1,5,11,19,21,23,27,45,51,65} {3,7,9,13,15,17,25,33,57,69}
2032933777875 {1,5,13,15,17,21,33,45,57,69} {3,7,9,11,19,23,25,27,51,65}
2032933777875 {1,5,13,15,19,21,33,45,51,69} {3,7,9,11,17,23,25,27,57,65}
2032933777875 {1,5,13,15,21,23,33,45,51,57} {3,7,9,11,17,19,25,27,65,69}
2032933777875 {1,5,13,17,21,25,27,33,57,69} {3,7,9,11,15,19,23,45,51,65}
2032933777875 {1,5,13,19,21,25,27,33,51,69} {3,7,9,11,15,17,23,45,57,65}
2032933777875 {1,5,13,21,23,25,27,33,51,57} {3,7,9,11,15,17,19,45,65,69}
2032933777875 {1,5,15,17,19,21,27,33,65,69} {3,7,9,11,13,23,25,45,51,57}
2032933777875 {1,5,15,17,21,23,27,33,57,65} {3,7,9,11,13,19,25,45,51,69}
2032933777875 {1,5,15,19,21,23,27,33,51,65} {3,7,9,11,13,17,25,45,57,69}
2032933777875 {1,5,17,19,21,23,27,33,45,65} {3,7,9,11,13,15,25,51,57,69}
2032933777875 {1,7,9,11,13,25,45,51,57,69} {3,5,15,17,19,21,23,27,33,65}
2032933777875 {1,7,9,11,15,17,45,57,65,69} {3,5,13,19,21,23,25,27,33,51}
2032933777875 {1,7,9,11,15,19,45,51,65,69} {3,5,13,17,21,23,25,27,33,57}
2032933777875 {1,7,9,11,15,23,45,51,57,65} {3,5,13,17,19,21,25,27,33,69}
2032933777875 {1,7,9,11,17,25,27,57,65,69} {3,5,13,15,19,21,23,33,45,51}
2032933777875 {1,7,9,11,19,25,27,51,65,69} {3,5,13,15,17,21,23,33,45,57}
2032933777875 {1,7,9,11,23,25,27,51,57,65} {3,5,13,15,17,19,21,33,45,69}
2032933777875 {1,7,9,13,15,25,33,51,57,69} {3,5,11,17,19,21,23,27,45,65}
2032933777875 {1,7,9,13,17,25,33,45,57,69} {3,5,11,15,19,21,23,27,51,65}
2032933777875 {1,7,9,13,19,25,33,45,51,69} {3,5,11,15,17,21,23,27,57,65}
2032933777875 {1,7,9,13,23,25,33,45,51,57} {3,5,11,15,17,19,21,27,65,69}
2032933777875 {1,7,9,15,17,19,33,45,65,69} {3,5,11,13,21,23,25,27,51,57}
2032933777875 {1,7,9,15,17,23,33,45,57,65} {3,5,11,13,19,21,25,27,51,69}
2032933777875 {1,7,9,15,19,23,33,45,51,65} {3,5,11,13,17,21,25,27,57,69}
2032933777875 {1,7,9,17,19,25,27,33,65,69} {3,5,11,13,15,21,23,45,51,57}
2032933777875 {1,7,9,17,23,25,27,33,57,65} {3,5,11,13,15,19,21,45,51,69}
2032933777875 {1,7,9,19,23,25,27,33,51,65} {3,5,11,13,15,17,21,45,57,69}
2032933777875 {1,7,11,13,15,25,27,51,57,69} {3,5,9,17,19,21,23,33,45,65}
2032933777875 {1,7,11,13,17,25,27,45,57,69} {3,5,9,15,19,21,23,33,51,65}
2032933777875 {1,7,11,13,19,25,27,45,51,69} {3,5,9,15,17,21,23,33,57,65}
2032933777875 {1,7,11,13,23,25,27,45,51,57} {3,5,9,15,17,19,21,33,65,69}
2032933777875 {1,7,11,15,17,19,27,45,65,69} {3,5,9,13,21,23,25,33,51,57}
2032933777875 {1,7,11,15,17,23,27,45,57,65} {3,5,9,13,19,21,25,33,51,69}
2032933777875 {1,7,11,15,19,23,27,45,51,65} {3,5,9,13,17,21,25,33,57,69}
2032933777875 {1,7,13,15,17,25,27,33,57,69} {3,5,9,11,19,21,23,45,51,65}
2032933777875 {1,7,13,15,19,25,27,33,51,69} {3,5,9,11,17,21,23,45,57,65}
2032933777875 {1,7,13,15,23,25,27,33,51,57} {3,5,9,11,17,19,21,45,65,69}
2032933777875 {1,7,13,17,19,25,27,33,45,69} {3,5,9,11,15,21,23,51,57,65}
2032933777875 {1,7,13,17,23,25,27,33,45,57} {3,5,9,11,15,19,21,51,65,69}
2032933777875 {1,7,13,19,23,25,27,33,45,51} {3,5,9,11,15,17,21,57,65,69}
2032933777875 {1,7,15,17,19,23,27,33,45,65} {3,5,9,11,13,21,25,51,57,69}
2032933777875 {1,9,11,13,15,21,25,51,57,69} {3,5,7,17,19,23,27,33,45,65}
2032933777875 {1,9,11,13,17,21,25,45,57,69} {3,5,7,15,19,23,27,33,51,65}
2032933777875 {1,9,11,13,19,21,25,45,51,69} {3,5,7,15,17,23,27,33,57,65}
2032933777875 {1,9,11,13,21,23,25,45,51,57} {3,5,7,15,17,19,27,33,65,69}
2032933777875 {1,9,11,15,17,19,21,45,65,69} {3,5,7,13,23,25,27,33,51,57}
2032933777875 {1,9,11,15,17,21,23,45,57,65} {3,5,7,13,19,25,27,33,51,69}
2032933777875 {1,9,11,15,19,21,23,45,51,65} {3,5,7,13,17,25,27,33,57,69}
2032933777875 {1,9,11,17,19,21,25,27,65,69} {3,5,7,13,15,23,33,45,51,57}
2032933777875 {1,9,11,17,21,23,25,27,57,65} {3,5,7,13,15,19,33,45,51,69}
2032933777875 {1,9,11,19,21,23,25,27,51,65} {3,5,7,13,15,17,33,45,57,69}
2032933777875 {1,9,13,15,17,21,25,33,57,69} {3,5,7,11,19,23,27,45,51,65}
2032933777875 {1,9,13,15,19,21,25,33,51,69} {3,5,7,11,17,23,27,45,57,65}
2032933777875 {1,9,13,15,21,23,25,33,51,57} {3,5,7,11,17,19,27,45,65,69}
2032933777875 {1,9,13,17,19,21,25,33,45,69} {3,5,7,11,15,23,27,51,57,65}
2032933777875 {1,9,13,17,21,23,25,33,45,57} {3,5,7,11,15,19,27,51,65,69}
2032933777875 {1,9,13,19,21,23,25,33,45,51} {3,5,7,11,15,17,27,57,65,69}
2032933777875 {1,9,15,17,19,21,23,33,45,65} {3,5,7,11,13,25,27,51,57,69}
2032933777875 {1,9,17,19,21,23,25,27,33,65} {3,5,7,11,13,15,45,51,57,69}
2032933777875 {1,11,13,15,17,21,25,27,57,69} {3,5,7,9,19,23,33,45,51,65}
2032933777875 {1,11,13,15,19,21,25,27,51,69} {3,5,7,9,17,23,33,45,57,65}
2032933777875 {1,11,13,15,21,23,25,27,51,57} {3,5,7,9,17,19,33,45,65,69}
2032933777875 {1,11,13,17,19,21,25,27,45,69} {3,5,7,9,15,23,33,51,57,65}
2032933777875 {1,11,13,17,21,23,25,27,45,57} {3,5,7,9,15,19,33,51,65,69}
2032933777875 {1,11,13,19,21,23,25,27,45,51} {3,5,7,9,15,17,33,57,65,69}
2032933777875 {1,11,15,17,19,21,23,27,45,65} {3,5,7,9,13,25,33,51,57,69}
2032933777875 {1,13,15,17,19,21,25,27,33,69} {3,5,7,9,11,23,45,51,57,65}
2032933777875 {1,13,15,17,21,23,25,27,33,57} {3,5,7,9,11,19,45,51,65,69}
2032933777875 {1,13,15,19,21,23,25,27,33,51} {3,5,7,9,11,17,45,57,65,69}
2032933777875 {1,13,17,19,21,23,25,27,33,45} {3,5,7,9,11,15,51,57,65,69}

王守恩 · 发表于 2024-5-14 07:13:35

2n个不同正奇数,  n个数的积=n个数的积。我们希望：积是最小的。

根据n=2,3,4,5,6,7,8,9,10的结论,我们能否这样考虑(我们只要这串数)？

(3*5) (3*5) (9*7/5) (5*11/3) (9*13/5) (5*7) (3*17*19/(5*7)) (5*7) (3*5*23/7) ......

又: 再来两串数, 一并解决了。

数字串(0): 2n个不同整数(最小=0),  n个数的和=n个数的和。我们希望：和是最小的。

数字串(1): 2n个不同整数(最小=1),  n个数的和=n个数的和。我们希望：和是最小的。

northwolves · 发表于 2024-5-14 13:19:04

数字串(1): 2n个不同整数(最小=1),  n个数的和=n个数的和。我们希望：和是最小的。

n=2k:  取1-4k 即可
n=2k+1:  取1-4k-1 即可

{5, 11, 18, 28, 39, 53, 68, 86, 105, 127, 150, 176, 203, 233, 264, 298, 333, 371...}
$a_n=\ceil[(2*n + 1)*n/2]$

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[求助] 有这样一串数(OEIS找不到)

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