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(5,8,44)
(5,20,40)
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(6,30,33)
(8,19,40)
(13,16,40)
(15,30,30)
(16,20,37)
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141414141414141414141414141497
15151515151515151515151515151501
1616161616161616161616161616161691
171717171717171717171717171717171737
118181818181818181818181818181818181881
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221_(4)=41
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3332_(5)=467
14444_(5)=1249
15_(6)=11
225_(6)=89
23335_(6)=3371
44441_(6)=6217
155555_(6)=15551
10_(7)=7
221_(7)=113
2333_(7)=857
14444_(7)=4001
455555_(7)=81233
6666665_(7)=823541
13_(8)=11
225_(8)=149
3331_(8)=1753
244447_(8)=84263
655555_(8)=220013
16666663_(8)=3894707
67777777_(8)=14680063
12_(9)=11
122_(9)=101
3332_(9)=2459
34444_(9)=22963
255555_(9)=155003
26666661_(9)=13153159
47777777_(9)=23316973
1488888888_(9)=602654093
No.2368kuiperbelt2024幎12æ6æ¥ 20:38
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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
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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
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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
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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

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39段ãïŒ00段ã10000段ãªã©ãšãã§ããªãããšãäºæ³ã§ããã
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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
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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
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No.2365ãããã2024幎12æ4æ¥ 14:07