______________ 3_________________
_____________ 1 4 ________________
____________ 1 5 9________________
____________2 6 5 3_______________
___________8 9 7 9 3______________
__________2 3 8 4 6 2_____________
_________ã.............. _____________
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é äžã®3ã®æ°åããæŸãå§ããŠå·ŠæãäžããŸãã¯å³æãäžããããã®æ°åãæŸããªãã
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ããããŠæäžæ®µã®æãŸã§æŸãéããæã®ãã®æŸã£ãæ°åã®åã®ããããã®æå€§å€ãšæå°å€ã¯ïŒ
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ã«ããŠããå Žåã®å±±ã§ã¯,ã¯ãŠãã®æã®æå€§å€ãšæå°å€ã¯ïŒ
ãªãæäžæ®µã¯
4,7,7,1,3,0,9,9,6,0,5,1,8,7,0,7,2,1,1,3,4,9,9,9,9,9,9,8,3,7,2,9,7,8,0,4,9,9,5 ã®äžŠã³ã§ãã
ã³ã³ãã¥ãŒã¿ã§ææŠããŠãããã ãå
šéšã§2^38=274877906944éãã®ã³ãŒã¹ãããã®ã§
éåžžã®æ€çŽ¢ããã°ã©ã ã§ã¯3æ¥éèšç®ããç¶ããŠããŸããæ¯ãç«ã¡ãŸããã
äœãããããã¯ãã©ãã¯æ³ãšããã€ã¯ã¹ãã©æ³ãªã©ã®ææ³ããããããšã¯æ¬ã§ã¯ç޹ä»
ãããŠããŸãããåŠäœãããããã䜿ãããªãç¥èãæã身ã«çããŠãããŸããã
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No.2347GAI2024幎11æ30æ¥ 17:49
ããã°ã©ã ãæ£ãããã°ãã§ãã
8段: æå°19ãæå€§50
9段: æå°20ãæå€§59
10段: æå°22ãæå€§67
39段: æå°76ãæå€§260
100段: æå°207ãæå€§693
1000段: æå°2055ãæå€§6964
10000段: æå°20334ãæå€§69638
äžæ®µãã€ïŒå
šèŠçŽ ããããã®ïŒæå°ãšæå€§ãæŽæ°ããŠãããšæ©ãã§ãã
No.2349ãããã2024幎11æ30æ¥ 23:16
æåæå€§å€,æå°å€ã®äœçœ®ã ãã«çç®ããã°ããã®ããšæã£ãã®ã§ãã
6段ãã7段ã§ã¯
6段ã§ã®æå€§å€38ã ãããããã¯å³æãäžã ãããå·Šæãäžã§ãå
±ã«3ãå ãããããªã
7段ã§ã®åèšã¯41ã§ããã
äžæ¹6段ã§ã®å34ã§ããå°ç¹(3ãæãã)ã®äžã€ããã¯34+8,34+3ãšããå¯èœæ§ãããåã®41
ãè¶ãããã42ãçºçããã
åŸã£ãŠãã åã«æå€§å€ãããäœçœ®ããæ¬¡ã®æå€§å€ãçºçããããšã«ãªããªãïŒïŒã§ãå¯èœæ§ã¯é«ã)
äžã«äžŠã¶æ°ã¯ååšçã®ããæå³ã©ã³ãã ãªæ°åã®åã§ããã®ã§ãçµå±ãã®æ¬¡ã®åãã©ããªããã¯
ããŒã¿ã«ã§èŠããããªãæ§ã«æãããŸããã
ããã§
a(n)=floor(Pi*10^(n-1))-10*floor(Pi*10^(n-2)) //ååšçã®å°æ°ç¹ä»¥äžç¬¬näœã«çŸããæ°å
f(k)=k*(k-1)/2+1
g(k)=k*(k+1)/2
ãå
ã«å®çŸ©ããŠãã
gp > L=List([3]);
gp > for(k=2,25,ã//ïœã¯ä¿µç©ã¿ã®æ®µã瀺ãã
for(n=1,#L,listinsert(L,L[2*n-1],2*n-1)); //Lã®é
åãåãæ°åãäºåºŠç¹°ãè¿ããŠäžŠã¹ãã
A=[];for(n=1,2^(k-1),A=concat(A,[hammingweight(2*n-1)]));ã//ä»ããäœçœ®ããã©ã¡ãã®ã³ãŒã¹ãžè¡ããã®éžæå¯èœãªäžŠã³ã
V=[];for(n=f(k),g(k),V=concat(V,[a(n)]));ã//æ¬¡ã®æ®µã«éãããšãã®å
·äœçæ°ïŒÏã®å°æ°ç¹ä»¥äžã®æ°ã®äžŠã³ã)
V=vecextract(V,A);ã//ã³ãŒã¹ã®æ¹åã«å¯Ÿå¿ããÏã®å°æ°éšåã®æ°åã«çœ®ãæããã
L=List(Vec(L)+V);ã//å2ã€ã®ã³ãŒã¹ã蟿ã£ããšãã«å
ããã®æ°åãšã®ã®åç¶æ
ã䞊ã¹ããã®ã次ã®ã¹ãããã§ã®åã§ã®é
åãšãªãã
print(k";"vecmin(Vec(L))" VS "vecmax(Vec(L))))ã//䞊ãã ãã¹ãŠã®åã®åè£ã§ã®æå°ãæå€§ãèŠã€ããã
2;4 VS 7
3;5 VS 16
4;7 VS 21
5;12 VS 30
6;14 VS 38
7;17 VS 42
8;19 VS 50
9;20 VS 59
10;22 VS 67
11;26 VS 76
12;26 VS 84
13;28 VS 88
14;28 VS 97
15;30 VS 102
16;30 VS 111
17;34 VS 115
18;35 VS 119
19;39 VS 128
20;43 VS 137
21;45 VS 143
22;46 VS 148
23;49 VS 154
24;50 VS 160
25;50 VS 166

ã䞊ã¶ãïŒãããŸã§3æéçšåºŠçµéããã)
äžæ®µããšã«æããæéã¯åã
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çã
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ã®æ®µã§ã®çµæãåŸããŸã§ã«ã¯ãè«å€§ãªæéãæããæ§åã«ãªã£ãŠããã
äŸãäžæ®µããšã®ç®åºæéãäžç¬ã§ãææ°é¢æ°çã«å¢å€§ããŠããèŠç©ããã§
39段ãïŒ00段ã10000段ãªã©ãšãã§ããªãããšãäºæ³ã§ããã
ããã
ããããããã¯äžäœã©ããªæã䜿ãã°ããããªèšå€§ãªæéãèŠããåé¡ã«å¯ŸåŠãããŠããã®ãïŒ
ãªãå¥ã®è¡åãå©çšããåå¥ã®ããæ¹ã§ã¯ïŒè¡åãžã®å
¥åãèªååã§ããªãæéãããã)
20段ïŒ24ç§çšåºŠ
21段ïŒ53ç§çšåºŠ
22段ïŒ1å50ç§çšåºŠ
23段ïŒ4åïŒç§çšåºŠ
24段ïŒ9å13ç§çšåºŠ
25段 ; 20å11ç§çšåºŠ
ã®çµéãªã®ã§ãåã®ããã°ã©ã ããã¹ããŒãã¢ããããŠãããã®å
åã
ãšãªããšãããæ¬çãšã¯æããªãã
No.2357GAI2024幎12æ3æ¥ 07:56
1段ç®(3)
æå°3ãæå€§3
2段ç®(1,4)
端ã¯åã«è¶³ããããªãã®ã§
1çªç®ã¯æå°=æå€§=3+1=4
2çªç®ã¯æå°=æå€§=3+4=7
3段ç®(1,5,9)
1çªç®ã¯æå°=æå€§=4+1=5
2çªç®ã¯
äžã®æ®µã®å·ŠåŽã®æå°ã¯4ãå³åŽã®æå°ã¯7ã§4ã®æ¹ãå°ããã®ã§æå°4+5=9
äžã®æ®µã®å·ŠåŽã®æå€§ã¯4ãå³åŽã®æå€§ã¯7ã§7ã®æ¹ã倧ããã®ã§æå€§7+5=12
3çªç®ã¯æå°=æå€§=7+9=16
3段ç®ãŸã§ã§
æå°5,9,16
æå€§5,12,16
4段ç®(2,6,5,3)
1çªç®ã¯æå°=æå€§=5+2=7
2çªç®ã¯
äžã®æ®µã®æå°ã®5ãš9ã§ã¯5ã®æ¹ãå°ããã®ã§æå°ã¯5+6=11
äžã®æ®µã®æå€§ã®5ãš12ã§ã¯12ã®æ¹ã倧ããã®ã§æå€§ã¯12+6=18
3çªç®ã¯
äžã®æ®µã®æå°ã®9ãš16ã§ã¯9ã®æ¹ãå°ããã®ã§æå°ã¯9+5=14
äžã®æ®µã®æå€§ã®12ãš16ã§ã¯16ã®æ¹ã倧ããã®ã§æå€§ã¯16+5=21
4çªç®ã¯æå°=æå€§=16+3=19
4段ç®ãŸã§ã§
æå°7,11,14,19
æå€§7,18,21,19
åæ§ã«5段ç®ã¯(5,8,9,7,9)ãªã®ã§æå°ãšæå€§ãæŽæ°ããŠ
æå°12,15,20,21,28
æå€§12,26,30,28,28
6段ç®ã¯(3,2,3,8,4,6)ãªã®ã§æå°ãšæå€§ãæŽæ°ããŠ
æå°15,14,18,28,25,34
æå€§15,28,33,38,32,34
7段ç®ã¯(2,6,4,3,3,8,3)ãªã®ã§æå°ãšæå€§ãæŽæ°ããŠ
æå°17,20,18,21,28,33,37
æå€§17,34,37,41,41,42,37
8段ç®ã¯(2,7,9,5,0,2,8,8)ãªã®ã§æå°ãšæå€§ãæŽæ°ããŠ
æå°19,24,27,23,21,30,41,45
æå€§19,41,46,46,41,44,50,45
åŸã£ãŠ8段ç®ãŸã§ã®æå°ãšæå€§ã¯ããããã®äžã§ã®æå°ãæå€§ã調ã¹ãããšã«ãã
æå°ã¯19ãæå€§ã¯50ãšããããŸãã
ã€ãŸãäžæ®µåŠçãããã³ã«ããã®èŠçŽ ãŸã§ã®çµè·¯ã®æå°å€ãšæå€§å€ãã
äžæ®µã®èŠçŽ æ°åèŠããŠãããŠæŽæ°ããŠããã°ã
100段ã§ã1000段ã§ããã£ãšããéã«çµãããŸããã
No.2358ãããã2024幎12æ3æ¥ 09:10
é
ãããŠããã®ã¯ååšçã®é
åããã¡ãã¡å
ã®Piããèšç®ã§éããŠããããšãšã
åºæ¥äžããåã®æ¹ã«ççŒç¹ãåããéããŠããŠãã©ãããŠã調æ»ç¯å²ã2åãïŒåãšåºãã£ãŠãã£ããšæ°ä»ããããŸããã
æ¬¡ã®æ®µã®ååšçã®æ°ã«å¯Ÿããããããã®æå°ãæå€§ã®å¯èœæ§ã®æ¹ã«èŠç¹ãåããããšã§ãã®æ®µã®åæ°åã®ããŒã¿ã ãã§æžãããã§ããã
ããã§ååšçã®å°æ°ç¹ä»¥äž6000æ¡ãŸã§ãDã§digitsåãããŠ(1+2+3++100=5050ãŸã§å°æ°ç¹ã䌞ã³ãã®ã§)
gp > P(n)=D[n*(n-1)/2..n*(n+1)/2-1]
ã®æŸãåãã§å®çŸ©ããããš
gp > S1=[5,9,16]
gp > S2=[5,12,16]
gp > for(r=4,100,S11=vector(r,i,0);S11[1]=P(r)[1]+S1[1];\
for(k=2,r-1,S11[k]=min(S1[k-1],S1[k])+P(r)[k]);\
S11[r]=P(r)[r]+S1[r-1];\
S22=vector(r,i,0);S22[1]=P(r)[1]+S2[1];
for(k=2,r-1,S22[k]=max(S2[k-1],S2[k])+P(r)[k]);\
S22[r]=P(r)[r]+S2[r-1];\
print(r";"vecmin(S11) " VS "vecmax(S22));S1=S11;S2=S22)
2;4 VS 7
3;5 VS 16
-----------
4;7 VS 21
5;12 VS 30
6;14 VS 38
7;17 VS 42
8;19 VS 50
9;20 VS 59
10;22 VS 67
11;26 VS 76
12;26 VS 84
13;28 VS 88
14;28 VS 97
15;30 VS 102
16;30 VS 111
17;34 VS 115
18;35 VS 119
19;39 VS 128
20;43 VS 137
21;45 VS 143
22;46 VS 148
23;49 VS 154
24;50 VS 160
25;50 VS 166
26;52 VS 175
27;52 VS 176
28;53 VS 185
29;53 VS 190
30;53 VS 198
31;61 VS 205
32;61 VS 211
33;61 VS 220
34;63 VS 227
35;65 VS 234
36;70 VS 241
37;72 VS 245
38;72 VS 253
39;76 VS 260
40;77 VS 268
41;77 VS 276
42;80 VS 283
43;81 VS 291
44;83 VS 300
45;83 VS 303
46;83 VS 310
47;88 VS 315
48;89 VS 321
49;91 VS 328
50;94 VS 337
51;97 VS 342
52;98 VS 349
53;101 VS 358
54;105 VS 366
55;109 VS 372
56;111 VS 379
57;112 VS 383
58;116 VS 392
59;118 VS 400
60;120 VS 406
61;123 VS 413
62;126 VS 422
63;128 VS 428
64;128 VS 436
65;131 VS 444
66;135 VS 453
67;137 VS 460
68;139 VS 467
69;142 VS 473
70;146 VS 481
71;146 VS 486
72;150 VS 495
73;154 VS 501
74;157 VS 508
75;157 VS 516
76;157 VS 525
77;158 VS 534
78;159 VS 541
79;162 VS 550
80;166 VS 559
81;171 VS 565
82;172 VS 574
83;174 VS 579
84;176 VS 586
85;181 VS 592
86;183 VS 597
87;185 VS 605
88;186 VS 613
89;186 VS 619
90;190 VS 625
91;190 VS 634
92;194 VS 638
93;194 VS 645
94;198 VS 654
95;199 VS 658
96;199 VS 665
97;202 VS 674
98;204 VS 678
99;207 VS 687
100;207 VS 693
time = 47 ms.
ã»ããšã«ã¢ããšèšãéã§ããã
No.2364GAI2024幎12æ4æ¥ 07:39
çããäžèŽããŠå®å¿ããŸããã
No.2365ãããã2024幎12æ4æ¥ 14:07
以åäºå¹³æ¹ååè§£ã®æçš¿ã§ãããåææ°Pãäžèšâ ã®æ§è³ªãæã€ãªãã°
b=[âP]ãïŒ[ã]ã¯ã¬ãŠã¹èšå·ïŒ
ã§bãæ±ãŸãäºãããããããã«æããŠé ããŸããã
â PïŒa^2+b^2
â»ãã ãa,bã¯èªç¶æ°ãbã¯(2Ã(aã®æ¡æ°)ïŒ1)æ¡ä»¥äžã®æ°
ãããšäŒŒããããªææ³ã§å¹³æ¹å·®ãæ±ããããäºãåãããŸããã
ããªãã¡
ããåææ°qãäžèšâ¡ã®æ§è³ªãæã€ãšã
x=[âq]+1ãïŒ[ã]ã¯ã¬ãŠã¹èšå·ïŒ
ã§xãæ±ãŸããããããå¹³æ¹å·®ãæ±ãããã
çµè«ãšããŠçŽ å æ°åè§£å¯èœã
â¡qïŒx^2-y^2
â»ãã ãx,yã¯èªç¶æ°ã§ãããxã¯(2Ã(yã®æ¡æ°)ïŒ1)æ¡ä»¥äžã®æ°
äŸïŒæ¬¡ã®â¢qãçŽ å æ°åè§£ãããã ã ãâ¡ã®æ§è³ªãæã€ãã®ãšããã
â¢q=975461057985063252585468007926206200262277
C=[âq]ãšããŠ
C=987654321098765432108
E=C+1ãšããŠ
E=987654321098765432109
E^2ãèšç®ããŠ
E^2=975461057985063252585526596557677488187881
F=E^2-qãšããŠ
F=975461057985063252585526596557677488187881
-975461057985063252585468007926206200262277
=58588631471287925604
âFãèšç®ããŠ
âF=7654321098
E+âFãèšç®ããŠ
E+âF=987654321098765432109+7654321098
=987654321106419753207
q/(E+âF)ãèšç®ããŠ
q/(E+âF)=975461057985063252585468007926206200262277
/987654321106419753207
=987654321091111111011ïŒå²ãåããïŒ
ãã£ãŠ
q=987654321106419753207Ã987654321091111111011
çµãã
No.2354inazuma_50683645,165655172024幎12æ1æ¥ 23:31
æ°åŠæåç§è©± > ç·æ¥ã®å æ°åè§£
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No.2355DD++2024幎12æ2æ¥ 07:53
DD++ãã
ã³ã¡ã³ãããããšãããããŸã
ç·æ¥ã®å æ°åè§£èªãŸããŠããã ããŸããã
"æ¯ã1ã«è¿ã2æ°ã®ç©ããå
ã®2æ°ãæ±ãã"
æ¹æ³ã§ã¯ããã®ã§ãããã©ããç§ãšããŠã¯
ãã®æ¯ãå°ãã§ãïŒããé ãããææ³ã
暡玢ããŠããæã§ãããŸãäœãé²å±ãããã°
æçš¿ãããŠããã ããããšæããŸãã
No.2356inazuma_50683645,165655172024幎12æ2æ¥ 19:52
[2305]ã®ç¶ãã§ãã
13人ããã°ãã®ãã¡æå€§ïŒåãåãã€ããŠã64æã®é貚ãåŠçã§ããã ãããã®ä»¶ã§ãã
æ¢ã«ã瀺ãããŸããããã«ãç¥äººããè§£ãæããŠããã£ããã®ã®ãã®èæ¯ã«ã¯äœãæãã®ãè§£ããã«åœ·åŸšã£ãŠãããŸãã
æ®éã«äœããš32æãéçã
挞ããã®ã»ã©å€ãè«æãã¿ã€ããŸããã
An optimum nonlinear code
code
Alan W. Nordstrom ,
John P. Robinson
https://www.sciencedirect.com/science/article/pii/S0019995867908352
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Yâ = Xâ â Xâ â Xâ â Xâ â ((Xâ â Xâ
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Yâ = Xâ â Xâ â Xâ â Xâ
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Yâ = Xâ â Xâ â Xâ â Xâ â ((Xâ â Xâ) â
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Yâ = Xâ â Xâ â Xâ
â Xâ â ((Xâ â Xâ) â
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Yâ
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Yâ = Xâ
â Xâ â Xâ â Xâ â ((Xâ â Xâ) â
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0000000000000
0000011001011
0000100010111
0000111100110
0001000101110
0001011111000
0001101001101
0001110100001
0010001011100
0010010101101
0010101110001
0010110111010
0011000011011
0011011110111
0011101000010
0011110010100
0100000111001
0100011010101
0100101011010
0100110001100
0101001100011
0101010010010
0101101110100
0101110111111
0110000110110
0110011100000
0110101101111
0110110000011
0111000000101
0111011001110
0111100101000
0111111011001
1000001110010
1000010011110
1000100101011
1000111111101
1001000110101
1001011000100
1001100011000
1001111010011
1010001000111
1010010010001
1010100100100
1010111001000
1011001101001
1011010100010
1011101111110
1011110001111
1100001101100
1100010100111
1100101000001
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1101001011111
1101010001001
1101100000110
1101111101010
1110000001010
1110011111011
1110100011101
1110111010110
1111001010000
1111010111100
1111100110011
1111111100101
No.2353Dengan kesaktian Indukmu2024幎12æ1æ¥ 18:05
æ±åå€§éŽæšçŠå
ææã®éæ¹é£ã®è±èªçã®ããŒãž
http://mathforum.com/te/exchange/hosted/suzuki/MagicSquare.html
ããªã³ã¯åãã«ãªã£ãŠããŸããããå
šéšã¯ç¢ºèªããŠããŸããããwebarchiveã§ãŸã é²èЧããããšã¯ã§ããããã§ãã
https://web.archive.org/web/20060709213003/http://mathforum.org/te/exchange/hosted/suzuki/MagicSquare.html
ããã®ä»€åïŒå¹ŽïŒæïŒïŒæ¥ä»ãã®ãè¶
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çŸãæ¥æ¬è©è«ç€ŸïŒã®ç¬¬8ç« ããããããªéæ¹é£ãã®p.276ã«å¥ã®è§£ãèŒã£ãŠããŸããã
No.2333kuiperbelt2024幎11æ23æ¥ 22:17
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20â17
17â20
18â19
19â18
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No.2337GAI2024幎11æ24æ¥ 07:27
kuiperbeltãããæžãããè§£ã¯æ¡ä»¶ãæºãããŠããªãæ°ãããŸãã
C1ã®ååšäž: 22+38+33+28+18+19+13+8+3+23 = 205
C2ã®ååšäž: 21+39+32+29+17+18+12+9+2+22 = 201
C3ã®ååšäž: 25+40+31+30+16+17+11+10+1+21 = 202
C4ã®ååšäž: 24+36+35+26+20+16+15+6+5+25 = 208
C5ã®ååšäž: 23+37+34+27+19+20+14+7+4+24 = 209
GAIãããæžãããããã«å
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šéš205ã«ãªããŸãã®ã§ã
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No.2338ãããã2024幎11æ24æ¥ 12:36
ãææã®ãšãã転èšãã¹ã ã£ãã®ã§èšæ£ããŠãããŸãã
No.2339kuiperbelt2024幎11æ24æ¥ 15:17
GAIããã®ãè¶
åæ¹é£ãã¯3ã€ã®åå¿åã«5ã€ã®åã亀差ããããã«ããã€ã5ã€ã®åã®ãã¡é£ãåã2ã€ã®åã亀差ããããã«é
眮ãããšãã«ã§ãã40åã®äº€ç¹ã«ã1ïœ40ã®æ°ãã2ã€ã®åã®äº€ç¹ã§ãã2ç¹ã«åã41ãšãªãããã«é
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ãããäžè¬åããŠãnåã®åå¿åã«(n+2)åã®åã亀差ããããã«ããã€ã(n+2)åã®åã®ãã¡é£ãåã2ã€ã®åã亀差ããããã«é
眮ãããšãã«ã§ãã2(n+1)(n+2)åã®äº€ç¹ã«ã1ïœ2(n+1)(n+2)ã®æ°ãã2ã€ã®åã®äº€ç¹ã§ãã2ç¹ã«åã2(n+1)(n+2)+1ãšãªãããã«é
眮ãããšãåäžã®2(n+2)ç¹ã®ç·åã(n+2)(2(n+1)(n+2)+1)ã®å®åãšãªããšãã(2n+2)åé£ãèããŠã¿ãŸããã
n=1ã®å Žåã¯4åé£ã§ã1ã€ã®åã«3åã®åã亀差ããããã«ããã€ã3åã®åã®ãã¡é£ãåã2ã€ã®åã亀差ããããã«é
眮ãããšãã«ã§ãã12åã®äº€ç¹ã«ã1ïœ12ã®æ°ãã2ã€ã®åã®äº€ç¹ã§ãã2ç¹ã«åã13ãšãªãããã«é
眮ãããšãåäžã®6ç¹ã®ç·åã39ã®å®åãšãªããšãããã®ã§ããéæ¹é£ã®äžç(倧森æž
çŸ)ãã®p.274ã®å³åŽã®4åé£ã§åã®å€§å°é¢ä¿ã調æŽãããã®ã«çžåœããŸãã
n=2ã®å Žåã¯6åé£ã§ã2åã®åå¿åã«4åã®åã亀差ããããã«ããã€ã4åã®åã®ãã¡é£ãåã2ã€ã®åã亀差ããããã«é
眮ãããšãã«ã§ãã24åã®äº€ç¹ã«ã1ïœ24ã®æ°ãã2ã€ã®åã®äº€ç¹ã§ãã2ç¹ã«åã25ãšãªãããã«é
眮ãããšãåäžã®8ç¹ã®ç·åã100ã®å®åãšãªããšãããã®ã§ããéæ¹é£ã®äžç(倧森æž
çŸ)ãã®p.275ã®å·ŠåŽã®6åé£ã§åã®å€§å°é¢ä¿ã調æŽãããã®ã«çžåœããŸãã
n=3ã®å Žåã®8åé£ããGAIããã®ãè¶
åæ¹é£ããšãªããŸãã
n=4ã®å Žåã¯10åé£ã§ã4åã®åå¿åã«6åã®åã亀差ããããã«ããã€ã6åã®åã®ãã¡é£ãåã2ã€ã®åã亀差ããããã«é
眮ãããšãã«ã§ãã60åã®äº€ç¹ã«ã1ïœ60ã®æ°ãã2ã€ã®åã®äº€ç¹ã§ãã2ç¹ã«åã61ãšãªãããã«é
眮ãããšãåäžã®12ç¹ã®ç·åã366ã®å®åãšãªããšãããã®ã§ãã
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No.2350kuiperbelt2024幎12æ1æ¥ 16:34
4åé£
No.2351kuiperbelt2024幎12æ1æ¥ 16:37
6åé£
No.2352kuiperbelt2024幎12æ1æ¥ 16:39
1/(k*(k+1)*(k+2))=(1/2)*(1/(k*(k+1))-1/((k+1)*(k+2)))
1/(k*(k+1)*(k+2)*(k+3))=(1/3)*(1/(k*(k+1)*(k+2))-1/((k+1)*(k+2)*(k+3)))
...
1/(k*(k+1)*(k+2)*...*(k+m))=(1/m)*(1/(k*(k+1)*...*(k+m-1))-1/((k+1)*(k+2)*...*(k+m)))
ãªã®ã§ã
1/(1*2*3)+1/(2*3*4)+...+1/(n*(n+1)*(n+2))=(1/2)*(1/(1*2)-1/((n+1)*(n+2)))
1/(1*2*3*4)+1/(2*3*4*5)+...+1/(n*(n+1)*(n+2)*(n+3))=(1/3)*(1/(1*2*3)-1/((n+1)*(n+2)*(n+3)))
...
1/(1*2*3*...*(m+1))+...+1/(n*(n+1)*(n+2)*...*(n+m))=(1/m)*(1/m!-n!/(n+m)!)
ãšããã®ããããŸããã
No.2346kuiperbelt2024幎11æ26æ¥ 00:41
äžå®ã®éå¹
ãæã€éè·¯ã®äž¡é£ã«ã¯ïŒã€ã®åçŽãªå£ãç«ã¡ã¯ã ãã
ä»äž¡å£ã«äºæ¬ã®æ¢¯åïŒé·ããx,yãšããã)ã亀差ãã圢ã§ç«ãŠãããããŠ
ãããã®ãšãããã®äº€å·®ããŠããå Žæã®éè·¯ããã®é«ããhãšãããšã
ãããããéè·¯ã®å¹
wãç®åºãããã®ãšããã(梯åã¯éã®äž¡ç«¯ããããããå察åŽã®å£ã«æããããŠãããšããã)
1âŠ<x<yâŠ200ã§ããx,yãšhãå
šãп޿°ã§ããæãéå¹
ïœãæŽæ°ã§æ±ºå®ã§ããæŽæ°
(x,y,h)ã®çµåããæ¢ãåºããŠã»ããã
äžäŸ
(x,y,h)=(70,119,30)ã®æw=56ã§æ±ãŸãã
æŽã«
1âŠx<yâŠ1000ã®æ¡ä»¶x,yã®æŽæ°ã§
ãããŠhã®å€ãæŽæ°ã§ããæãéå¹
wãæŽæ°ãšãªããç°ãªãwã®å€ã¯äœéãå¯èœãïŒ
No.2341GAI2024幎11æ25æ¥ 10:05
ããã°ã©ã ãæ£ãããã°
1âŠxïŒyâŠ200ã§ã¯
(x,y,h,w)=(70,119,30,56),(74,182,21,70),(87,105,35,63),(100,116,35,80),(119,175,40,105)
ã®5çµ (wã5éã)
1âŠxïŒyâŠ1000ã§ã¯ çµåãã¯77éããwã¯53éã
ã€ãã§ã«
1âŠxïŒyâŠ10000ã§ã¯ çµåãã¯1440éããwã¯632éã
1âŠxïŒyâŠ100000ã§ã¯ çµåãã¯18612éããwã¯6423éã
(远èš)
ã¡ãªã¿ã«åœ¢ãèããŠhãšwã®æ¯ã«æ³šç®ããŠã¿ããš
100000ãŸã§ã§h/wãæå€§ã§ãããã®ã¯
(57739,87989,34713,6061) (h/wâ5.73)
100000ãŸã§ã§w/hãæå€§ã§ãããã®ã¯
(10817,23999,206,10815) (w/h=52.5)
åŸè
ã¯æ¢¯åã10.817mãšããŠéå¹
ãšã®å·®ã2mmãªã®ã§
å®éã«ã¯ç¡çããã§ããã
ãŸã
100000ãŸã§ã§y/xãæå€§ã§ãããã®ã¯
(169,7081,118,119) (y/xâ41.9)
æå°ã§ãããã®ã¯
(83259,83358,2378,83160) (y/xâ1.0012)
ãšãªã£ãŠããŸããã
No.2342ãããã2024幎11æ25æ¥ 14:56
èªåãªãã«èª¿æ»ããŠãæ£è§£ã¯ããããªïŒ
ã®ç¶æ
ã§åºé¡ããŠãã®ã§ãããããããããã®è§£çãšåããã®ã§ãã£ãšã»ã£ãšããŸãã
5/5=1
53/77=0.68831168831
632/1440=0.43888888888
6423/18612=0.34509993552
ã§å²åããæžå°ããŠãããã ãªã
No.2343GAI2024幎11æ25æ¥ 18:28
è§£ãçºãããšãæå°è§£ã®å®æ°åã®ãã®ãå€ãæ¬è³ªçã«ç°ãªãè§£ã§ã¯ãªãã®ã§
gcd(x,y,h,w)=1ã®è§£ã«éããš
200ãŸã§: çµåã5éããéå¹
5éã
1000ãŸã§: çµåã28éããéå¹
23éã
10000ãŸã§: çµåã263éããéå¹
221éã
100000ãŸã§: çµåã1613éããéå¹
1283éã
ã®ããã«ãªã£ãŠããŸããã
1000ãŸã§ã®çµåãã¯ä»¥äžã®éãã§ãã
(x,y,h,w)=(87,105,35,63),(100,116,35,80),(70,119,30,56),(119,175,40,105),(74,182,21,70),
(182,210,45,168),(156,219,44,144),(113,238,14,112),(175,273,90,105),(104,296,35,96),
(175,364,80,140),(58,401,38,40),(273,420,80,252),(187,429,72,165),(425,442,70,408),
(375,500,144,300),(195,533,120,117),(286,561,90,264),(533,650,90,520),(87,663,55,63),
(663,689,168,585),(365,715,176,275),(625,750,126,600),(275,814,70,264),(583,825,210,495),
(845,870,306,600),(429,915,275,165),(697,986,126,680)
No.2344ãããã2024幎11æ25æ¥ 18:50
確ãã«æå°è§£ã®å®æ°åã®ãã®ãã«ãŠã³ããããŠããŸã£ãŠããŸããã
gp > 23/28.
%210 = 0.82142857142857142857142857142857142857142857142857
gp > 221/263.
%211 = 0.84030418250950570342205323193916349809885931558935
gp > 1283/1613.
%212 = 0.79541227526348419094854308741475511469311841289523
ã§éã«åãwã«å¯Ÿãã2éãã®ãã¿ãŒã³æ°ã®æ¯çã¯äœãå€ãããªãã®ããã
1000ãŸã§ã®ç¯å²ã§ã¯
w=63ã«ã¯(x,y,h)=(87,105,35),(87,663,55)
w=105ã«ã¯(x,y,h)=(119,175,40),(175,273,90)
w=165ã«ã¯(x,y,h)=(187,429,72),(429,915,275)
w=264ã«ã¯(x,y,h)=(275,814,70),(286,561,90)
w=600ã«ã¯(x,y,h)=(625,750,126),(845,870,306)
ããããã2éãã®ãã¿ãŒã³ãèµ·ãããã§ããã
w=63ã®2ãã¿ãŒã³ã¯87ãå
±éã§è峿·±ãã§ãã
No.2345GAI2024幎11æ25æ¥ 20:11
éåé£ãšãã£ãŠãåå¿åãšçŽåŸãåãæ°ã ãæžããŠããã®äº€ç¹2n^2+1åã«æ°åã眮ããã®ããããŸãããçŽåŸäžã®2n+1åã®æ°åã®åïŒåŸåïŒãšãååšäžã®2nåã®æ°ãšäžå¿æ°ã®2n+1åã®æ°ã®å(åšå)ãå
šãŠçãããããã®ã§ããæ¥èŒç®æ³ãã«ã¯ãäžå¿ã®æ°ã9ãšããŠã4ã€ã®åå¿åäžã«{7,22,10,24,25,18,2,30},{19,13,23,3,11,26,29,14},{31,1,16,15,5,17,32,21},{12,33,20,27,28,8,6,4}ãé
ãã4æ¬ã®çŽåŸäžã«{12,31,19,7,9,25,11,5,28},{33,1,13,22,9,18,26,17,8},{20,16,23,10,9,2,29,32,6},{27,15,3,24,9,30,14,21,4}ãšãããæ
ä¹å³ããšããå³ãèŒã£ãŠããŸã(ãæ
ä¹ãã¯9ã«éãŸããšããæå³ã)ã
ãããå¿çšããŠãå³ã®ããã«å極ãšå極ã§äº€å·®ãã3ã€ã®å€§åãšãèµ€éãåç·¯45床ãåç·¯45床ã®3ã€ã®ç·¯ç·ã®åã®äº€ç¹ãšãªã20åã®ç¹ã«ã1ïœ20ã®æ°åãããã3ã€ã®å€§åäžã®æ°ã®åãšã3ã€ã®ç·¯ç·ã®åäžã®æ°ãšäž¡æ¥µã®æ°ã®åãå³ã®ããã«çãããããéçé£ããèããŠã¿ãŸããã1ïœ20ã®æ°åã®é
眮ã§ãå³ã®äž¡æ¥µã4ãš8ã®å Žåã®ä»ã«ãäž¡æ¥µã®æ°åãã©ã®ãããªãã®ãããã§ããããã
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No.2334kuiperbelt2024幎11æ23æ¥ 22:22
äž¡æ¥µã«æ¬¡ã®2ã€ã®æ°åãé
眮ããŠããã°ãä»ã®6çµã®åã=>ã§ã®å€ïŒèªç¶æ°)ã«ããæ®ãã®æ°åãã¡ããã©2床ãã€åºçŸãããããª
6çµã®6åãã€ã®æ°åã®çµåãã¯å±±ã»ã©æ§æå¯èœãšãªããšæããŸãã
1;1,2=>69
2;1,5=>68
3;1,8=>67
4;1,11=>66
5;1,14=>65
6;1,17=>64
7;1,20=>63
8;2,4=>68
9;2,7=>67
10;2,10=>66
11;2,13=>65
12;2,16=>64
13;2,19=>63
14;3,6=>67
15;3,9=>66
16;3,12=>65
17;3,15=>64
18;3,18=>63
19;4,5=>67
20;4,8=>66 (äŸã®å³ã®ãã¿ãŒã³)
21;4,11=>65
22;4,14=>64
23;4,17=>63
24;4,20=>62
25;5,7=>66
26;5,10=>65
27;5,13=>64
28;5,16=>63
29;5,19=>62
30;6,9=>65
31;6,12=>64
32;6,15=>63
33;6,18=>62
34;7,8=>65
35;7,11=>64
36;7,14=>63
37;7,17=>62
38;7,20=>61
39;8,10=>64
40;8,13=>63
41;8,16=>62
42;8,19=>61
43;9,12=>63
44;9,15=>62
45;9,18=>61
46;10,11=>63
47;10,14=>62
48;10,17=>61
49;10,20=>60
50;11,13=>62
51;11,16=>61
52;11,19=>60
53;12,15=>61
54;12,18=>60
55;13,14=>61
56;13,17=>60
57;13,20=>59
58;14,16=>60
59;14,19=>59
60;15,18=>59
61;16,17=>59
62;16,20=>58
63;17,19=>58
64;19,20=>57
No.2340GAI2024幎11æ25æ¥ 05:30
ãæ£å£«ããã¥ãŒ70幎ã®å è€äžäºäžä¹æ®µ(84)ãè©°ãå°æ£åºé¡65幎éç¶ç¶ã§ã®ãã¹èšé²ãã£ãŠå
šæ°å綺éºã«åºãŠããªãããšãã倧çºèŠãShiromaruããã«ãã£ãŠX(æ§ãã€ãã¿ãŒ)ã§å ±åãã話é¡ãšãªããŸãããURLã¯ä»¥äžã
x.com/siromaru460/status/1859445122246816091?t=ZZ_dzmTIWt4uTDqThlkKCA&s=19
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eâ(1+0.2^(9^(7Ã6)))^(5^(3^(84)))
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4450å0188äž7164æ¡ãŸã§äžèŽããè¿äŒŒå€
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åŒçšã¯ x.com/Science_Release/status/1859877878701424740?t=O15lpwQYZYWpwwlEeZCTYw&s=19 ããã
Daniel Bambergerã«ãããªãªãžãã«ã¯ãã®æçš¿ã®Denganã®ååã®URLãžã£ã³ãã®å
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â» 0.2=1/5ã ããã
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N=5^(3^84)ã«å¯ŸããŠ
eâ(1+1/N)^N
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No.2330Dengan kesaktian Indukmu2024幎11æ23æ¥ 10:35 1ïœïŒã«ãã ãã£ãŠã¿ãŸããã
(15768/3942)Ã(12345/9876)=13485/2697
(18534/9267)Ã(17469/5823)=34182/5697
(17469/5823)Ã(31689/4527)Ã(65934/1782)=748251/963=615384/792
ãªãæããã«æçš¿ãããŠããèšäºãã¡ã¢ããŠããããŒããèŠçŽããŠããã
ãã¶ã2017幎ãã
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eâ(1+.2^(3^84))^(5^(9^(6*7)))
ãæçš¿ãããŠãããšæããŸãã
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(1+9^(-4^(6*7)))^(3^(2^85))
(1+2^(-76))^(4^38+.5)
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i+s+x=6
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[ E, F, G, H, I, L, N, O, R, S, T, U, V, W, X, Z]=
1;[3/4, 15/4, 3, -11/4, 5/4, 6, 7/2, -13/4, -3/2, 11/4, 23/4, 5, -3/4, -1/2, 2, 4]
2;[9/4, 17/4, 3, -17/4, 7/4, 5, 5/2, -15/4, -5/2, 13/4, 21/4, 6, -13/4, 1/2, 1, 4]
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