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楼主: 王守恩

[原创] 数字串的通项公式

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 楼主| 发表于 2020-6-8 19:56:06 | 显示全部楼层
dlpg070 发表于 2020-4-4 07:45
在《阿里巴巴数学竞赛预选赛第二轮》造了一串数,你已经看到错了
毒酒滴冻鸭的分析水平很高,
这是个有 ...

可以有通项吗?
02=1,1
04=1,2
06=2,1
08=1,3
10=2,2
12=3,1
14=1,4
16=2,3
18=3,2
20=4,1
22=1,5
24=2,4
26=3,3
28=4,2
30=5,1
32=1,6
34=2,5
36=3,4
38=4,3
40=5,2
42=6,1
2020=?,?
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2020-6-9 09:45:22 | 显示全部楼层
本帖最后由 dlpg070 于 2020-6-9 09:49 编辑
王守恩 发表于 2020-6-8 19:56
可以有通项吗?
02=1,1
04=1,2


2020= 20,26

代码如下
  1. Clear["Global`*"]
  2. blist = Table[Range[n], {n, 45}] ;
  3. clist = Table[Reverse[blist[[n]]], {n, 1, Length[blist]}];
  4. blist = blist // Flatten;
  5. clist = clist // Flatten;

  6. out = Table[{n, 2*n, "=", blist[[n]], ",", clist[[n]]}, {n, 1,
  7.     Length[blist]}];
  8. Grid[out, Alignment -> Left]
复制代码


输出结果:
\(\(\begin{array}{llllll}
1 & 2 & = & 1 & , & 1 \\
2 & 4 & = & 1 & , & 2 \\
3 & 6 & = & 2 & , & 1 \\
4 & 8 & = & 1 & , & 3 \\
5 & 10 & = & 2 & , & 2 \\
6 & 12 & = & 3 & , & 1 \\
7 & 14 & = & 1 & , & 4 \\
8 & 16 & = & 2 & , & 3 \\
9 & 18 & = & 3 & , & 2 \\
10 & 20 & = & 4 & , & 1 \\
11 & 22 & = & 1 & , & 5 \\
12 & 24 & = & 2 & , & 4 \\
13 & 26 & = & 3 & , & 3 \\
14 & 28 & = & 4 & , & 2 \\
15 & 30 & = & 5 & , & 1 \\
16 & 32 & = & 1 & , & 6 \\
17 & 34 & = & 2 & , & 5 \\
18 & 36 & = & 3 & , & 4 \\
19 & 38 & = & 4 & , & 3 \\
20 & 40 & = & 5 & , & 2 \\
21 & 42 & = & 6 & , & 1 \\
22 & 44 & = & 1 & , & 7 \\
23 & 46 & = & 2 & , & 6 \\
24 & 48 & = & 3 & , & 5 \\
25 & 50 & = & 4 & , & 4 \\
26 & 52 & = & 5 & , & 3 \\
27 & 54 & = & 6 & , & 2 \\
28 & 56 & = & 7 & , & 1 \\
29 & 58 & = & 1 & , & 8 \\
30 & 60 & = & 2 & , & 7 \\
31 & 62 & = & 3 & , & 6 \\
32 & 64 & = & 4 & , & 5 \\
33 & 66 & = & 5 & , & 4 \\
34 & 68 & = & 6 & , & 3 \\
35 & 70 & = & 7 & , & 2 \\
36 & 72 & = & 8 & , & 1 \\
37 & 74 & = & 1 & , & 9 \\
38 & 76 & = & 2 & , & 8 \\
39 & 78 & = & 3 & , & 7 \\
40 & 80 & = & 4 & , & 6 \\
41 & 82 & = & 5 & , & 5 \\
42 & 84 & = & 6 & , & 4 \\
43 & 86 & = & 7 & , & 3 \\
44 & 88 & = & 8 & , & 2 \\
45 & 90 & = & 9 & , & 1 \\
46 & 92 & = & 1 & , & 10 \\
47 & 94 & = & 2 & , & 9 \\
48 & 96 & = & 3 & , & 8 \\
49 & 98 & = & 4 & , & 7 \\
50 & 100 & = & 5 & , & 6 \\
51 & 102 & = & 6 & , & 5 \\
52 & 104 & = & 7 & , & 4 \\
53 & 106 & = & 8 & , & 3 \\
54 & 108 & = & 9 & , & 2 \\
55 & 110 & = & 10 & , & 1 \\
56 & 112 & = & 1 & , & 11 \\
57 & 114 & = & 2 & , & 10 \\
58 & 116 & = & 3 & , & 9 \\
59 & 118 & = & 4 & , & 8 \\
60 & 120 & = & 5 & , & 7 \\
61 & 122 & = & 6 & , & 6 \\
62 & 124 & = & 7 & , & 5 \\
63 & 126 & = & 8 & , & 4 \\
64 & 128 & = & 9 & , & 3 \\
65 & 130 & = & 10 & , & 2 \\
66 & 132 & = & 11 & , & 1 \\
67 & 134 & = & 1 & , & 12 \\
68 & 136 & = & 2 & , & 11 \\
69 & 138 & = & 3 & , & 10 \\
70 & 140 & = & 4 & , & 9 \\
71 & 142 & = & 5 & , & 8 \\
72 & 144 & = & 6 & , & 7 \\
73 & 146 & = & 7 & , & 6 \\
74 & 148 & = & 8 & , & 5 \\
75 & 150 & = & 9 & , & 4 \\
76 & 152 & = & 10 & , & 3 \\
77 & 154 & = & 11 & , & 2 \\
78 & 156 & = & 12 & , & 1 \\
79 & 158 & = & 1 & , & 13 \\
80 & 160 & = & 2 & , & 12 \\
81 & 162 & = & 3 & , & 11 \\
82 & 164 & = & 4 & , & 10 \\
83 & 166 & = & 5 & , & 9 \\
84 & 168 & = & 6 & , & 8 \\
85 & 170 & = & 7 & , & 7 \\
86 & 172 & = & 8 & , & 6 \\
87 & 174 & = & 9 & , & 5 \\
88 & 176 & = & 10 & , & 4 \\
89 & 178 & = & 11 & , & 3 \\
90 & 180 & = & 12 & , & 2 \\
91 & 182 & = & 13 & , & 1 \\
92 & 184 & = & 1 & , & 14 \\
93 & 186 & = & 2 & , & 13 \\
94 & 188 & = & 3 & , & 12 \\
95 & 190 & = & 4 & , & 11 \\
96 & 192 & = & 5 & , & 10 \\
97 & 194 & = & 6 & , & 9 \\
98 & 196 & = & 7 & , & 8 \\
99 & 198 & = & 8 & , & 7 \\
100 & 200 & = & 9 & , & 6 \\
101 & 202 & = & 10 & , & 5 \\
102 & 204 & = & 11 & , & 4 \\
103 & 206 & = & 12 & , & 3 \\
104 & 208 & = & 13 & , & 2 \\
105 & 210 & = & 14 & , & 1 \\
106 & 212 & = & 1 & , & 15 \\
107 & 214 & = & 2 & , & 14 \\
108 & 216 & = & 3 & , & 13 \\
109 & 218 & = & 4 & , & 12 \\
110 & 220 & = & 5 & , & 11 \\
111 & 222 & = & 6 & , & 10 \\
112 & 224 & = & 7 & , & 9 \\
113 & 226 & = & 8 & , & 8 \\
114 & 228 & = & 9 & , & 7 \\
115 & 230 & = & 10 & , & 6 \\
116 & 232 & = & 11 & , & 5 \\
117 & 234 & = & 12 & , & 4 \\
118 & 236 & = & 13 & , & 3 \\
119 & 238 & = & 14 & , & 2 \\
120 & 240 & = & 15 & , & 1 \\
121 & 242 & = & 1 & , & 16 \\
122 & 244 & = & 2 & , & 15 \\
123 & 246 & = & 3 & , & 14 \\
124 & 248 & = & 4 & , & 13 \\
125 & 250 & = & 5 & , & 12 \\
126 & 252 & = & 6 & , & 11 \\
127 & 254 & = & 7 & , & 10 \\
128 & 256 & = & 8 & , & 9 \\
129 & 258 & = & 9 & , & 8 \\
130 & 260 & = & 10 & , & 7 \\
131 & 262 & = & 11 & , & 6 \\
132 & 264 & = & 12 & , & 5 \\
133 & 266 & = & 13 & , & 4 \\
134 & 268 & = & 14 & , & 3 \\
135 & 270 & = & 15 & , & 2 \\
136 & 272 & = & 16 & , & 1 \\
137 & 274 & = & 1 & , & 17 \\
138 & 276 & = & 2 & , & 16 \\
139 & 278 & = & 3 & , & 15 \\
140 & 280 & = & 4 & , & 14 \\
141 & 282 & = & 5 & , & 13 \\
142 & 284 & = & 6 & , & 12 \\
143 & 286 & = & 7 & , & 11 \\
144 & 288 & = & 8 & , & 10 \\
145 & 290 & = & 9 & , & 9 \\
146 & 292 & = & 10 & , & 8 \\
147 & 294 & = & 11 & , & 7 \\
148 & 296 & = & 12 & , & 6 \\
149 & 298 & = & 13 & , & 5 \\
150 & 300 & = & 14 & , & 4 \\
151 & 302 & = & 15 & , & 3 \\
152 & 304 & = & 16 & , & 2 \\
153 & 306 & = & 17 & , & 1 \\
154 & 308 & = & 1 & , & 18 \\
155 & 310 & = & 2 & , & 17 \\
156 & 312 & = & 3 & , & 16 \\
157 & 314 & = & 4 & , & 15 \\
158 & 316 & = & 5 & , & 14 \\
159 & 318 & = & 6 & , & 13 \\
160 & 320 & = & 7 & , & 12 \\
161 & 322 & = & 8 & , & 11 \\
162 & 324 & = & 9 & , & 10 \\
163 & 326 & = & 10 & , & 9 \\
164 & 328 & = & 11 & , & 8 \\
165 & 330 & = & 12 & , & 7 \\
166 & 332 & = & 13 & , & 6 \\
167 & 334 & = & 14 & , & 5 \\
168 & 336 & = & 15 & , & 4 \\
169 & 338 & = & 16 & , & 3 \\
170 & 340 & = & 17 & , & 2 \\
171 & 342 & = & 18 & , & 1 \\
172 & 344 & = & 1 & , & 19 \\
173 & 346 & = & 2 & , & 18 \\
174 & 348 & = & 3 & , & 17 \\
175 & 350 & = & 4 & , & 16 \\
176 & 352 & = & 5 & , & 15 \\
177 & 354 & = & 6 & , & 14 \\
178 & 356 & = & 7 & , & 13 \\
179 & 358 & = & 8 & , & 12 \\
180 & 360 & = & 9 & , & 11 \\
181 & 362 & = & 10 & , & 10 \\
182 & 364 & = & 11 & , & 9 \\
183 & 366 & = & 12 & , & 8 \\
184 & 368 & = & 13 & , & 7 \\
185 & 370 & = & 14 & , & 6 \\
186 & 372 & = & 15 & , & 5 \\
187 & 374 & = & 16 & , & 4 \\
188 & 376 & = & 17 & , & 3 \\
189 & 378 & = & 18 & , & 2 \\
190 & 380 & = & 19 & , & 1 \\
191 & 382 & = & 1 & , & 20 \\
192 & 384 & = & 2 & , & 19 \\
193 & 386 & = & 3 & , & 18 \\
194 & 388 & = & 4 & , & 17 \\
195 & 390 & = & 5 & , & 16 \\
196 & 392 & = & 6 & , & 15 \\
197 & 394 & = & 7 & , & 14 \\
198 & 396 & = & 8 & , & 13 \\
199 & 398 & = & 9 & , & 12 \\
200 & 400 & = & 10 & , & 11 \\
201 & 402 & = & 11 & , & 10 \\
202 & 404 & = & 12 & , & 9 \\
203 & 406 & = & 13 & , & 8 \\
204 & 408 & = & 14 & , & 7 \\
205 & 410 & = & 15 & , & 6 \\
206 & 412 & = & 16 & , & 5 \\
207 & 414 & = & 17 & , & 4 \\
208 & 416 & = & 18 & , & 3 \\
209 & 418 & = & 19 & , & 2 \\
210 & 420 & = & 20 & , & 1 \\
211 & 422 & = & 1 & , & 21 \\
212 & 424 & = & 2 & , & 20 \\
213 & 426 & = & 3 & , & 19 \\
214 & 428 & = & 4 & , & 18 \\
215 & 430 & = & 5 & , & 17 \\
216 & 432 & = & 6 & , & 16 \\
217 & 434 & = & 7 & , & 15 \\
218 & 436 & = & 8 & , & 14 \\
219 & 438 & = & 9 & , & 13 \\
220 & 440 & = & 10 & , & 12 \\
221 & 442 & = & 11 & , & 11 \\
222 & 444 & = & 12 & , & 10 \\
223 & 446 & = & 13 & , & 9 \\
224 & 448 & = & 14 & , & 8 \\
225 & 450 & = & 15 & , & 7 \\
226 & 452 & = & 16 & , & 6 \\
227 & 454 & = & 17 & , & 5 \\
228 & 456 & = & 18 & , & 4 \\
229 & 458 & = & 19 & , & 3 \\
230 & 460 & = & 20 & , & 2 \\
231 & 462 & = & 21 & , & 1 \\
232 & 464 & = & 1 & , & 22 \\
233 & 466 & = & 2 & , & 21 \\
234 & 468 & = & 3 & , & 20 \\
235 & 470 & = & 4 & , & 19 \\
236 & 472 & = & 5 & , & 18 \\
237 & 474 & = & 6 & , & 17 \\
238 & 476 & = & 7 & , & 16 \\
239 & 478 & = & 8 & , & 15 \\
240 & 480 & = & 9 & , & 14 \\
241 & 482 & = & 10 & , & 13 \\
242 & 484 & = & 11 & , & 12 \\
243 & 486 & = & 12 & , & 11 \\
244 & 488 & = & 13 & , & 10 \\
245 & 490 & = & 14 & , & 9 \\
246 & 492 & = & 15 & , & 8 \\
247 & 494 & = & 16 & , & 7 \\
248 & 496 & = & 17 & , & 6 \\
249 & 498 & = & 18 & , & 5 \\
250 & 500 & = & 19 & , & 4 \\
251 & 502 & = & 20 & , & 3 \\
252 & 504 & = & 21 & , & 2 \\
253 & 506 & = & 22 & , & 1 \\
254 & 508 & = & 1 & , & 23 \\
255 & 510 & = & 2 & , & 22 \\
256 & 512 & = & 3 & , & 21 \\
257 & 514 & = & 4 & , & 20 \\
258 & 516 & = & 5 & , & 19 \\
259 & 518 & = & 6 & , & 18 \\
260 & 520 & = & 7 & , & 17 \\
261 & 522 & = & 8 & , & 16 \\
262 & 524 & = & 9 & , & 15 \\
263 & 526 & = & 10 & , & 14 \\
264 & 528 & = & 11 & , & 13 \\
265 & 530 & = & 12 & , & 12 \\
266 & 532 & = & 13 & , & 11 \\
267 & 534 & = & 14 & , & 10 \\
268 & 536 & = & 15 & , & 9 \\
269 & 538 & = & 16 & , & 8 \\
270 & 540 & = & 17 & , & 7 \\
271 & 542 & = & 18 & , & 6 \\
272 & 544 & = & 19 & , & 5 \\
273 & 546 & = & 20 & , & 4 \\
274 & 548 & = & 21 & , & 3 \\
275 & 550 & = & 22 & , & 2 \\
276 & 552 & = & 23 & , & 1 \\
277 & 554 & = & 1 & , & 24 \\
278 & 556 & = & 2 & , & 23 \\
279 & 558 & = & 3 & , & 22 \\
280 & 560 & = & 4 & , & 21 \\
281 & 562 & = & 5 & , & 20 \\
282 & 564 & = & 6 & , & 19 \\
283 & 566 & = & 7 & , & 18 \\
284 & 568 & = & 8 & , & 17 \\
285 & 570 & = & 9 & , & 16 \\
286 & 572 & = & 10 & , & 15 \\
287 & 574 & = & 11 & , & 14 \\
288 & 576 & = & 12 & , & 13 \\
289 & 578 & = & 13 & , & 12 \\
290 & 580 & = & 14 & , & 11 \\
291 & 582 & = & 15 & , & 10 \\
292 & 584 & = & 16 & , & 9 \\
293 & 586 & = & 17 & , & 8 \\
294 & 588 & = & 18 & , & 7 \\
295 & 590 & = & 19 & , & 6 \\
296 & 592 & = & 20 & , & 5 \\
297 & 594 & = & 21 & , & 4 \\
298 & 596 & = & 22 & , & 3 \\
299 & 598 & = & 23 & , & 2 \\
300 & 600 & = & 24 & , & 1 \\
301 & 602 & = & 1 & , & 25 \\
302 & 604 & = & 2 & , & 24 \\
303 & 606 & = & 3 & , & 23 \\
304 & 608 & = & 4 & , & 22 \\
305 & 610 & = & 5 & , & 21 \\
306 & 612 & = & 6 & , & 20 \\
307 & 614 & = & 7 & , & 19 \\
308 & 616 & = & 8 & , & 18 \\
309 & 618 & = & 9 & , & 17 \\
310 & 620 & = & 10 & , & 16 \\
311 & 622 & = & 11 & , & 15 \\
312 & 624 & = & 12 & , & 14 \\
313 & 626 & = & 13 & , & 13 \\
314 & 628 & = & 14 & , & 12 \\
315 & 630 & = & 15 & , & 11 \\
316 & 632 & = & 16 & , & 10 \\
317 & 634 & = & 17 & , & 9 \\
318 & 636 & = & 18 & , & 8 \\
319 & 638 & = & 19 & , & 7 \\
320 & 640 & = & 20 & , & 6 \\
321 & 642 & = & 21 & , & 5 \\
322 & 644 & = & 22 & , & 4 \\
323 & 646 & = & 23 & , & 3 \\
324 & 648 & = & 24 & , & 2 \\
325 & 650 & = & 25 & , & 1 \\
326 & 652 & = & 1 & , & 26 \\
327 & 654 & = & 2 & , & 25 \\
328 & 656 & = & 3 & , & 24 \\
329 & 658 & = & 4 & , & 23 \\
330 & 660 & = & 5 & , & 22 \\
331 & 662 & = & 6 & , & 21 \\
332 & 664 & = & 7 & , & 20 \\
333 & 666 & = & 8 & , & 19 \\
334 & 668 & = & 9 & , & 18 \\
335 & 670 & = & 10 & , & 17 \\
336 & 672 & = & 11 & , & 16 \\
337 & 674 & = & 12 & , & 15 \\
338 & 676 & = & 13 & , & 14 \\
339 & 678 & = & 14 & , & 13 \\
340 & 680 & = & 15 & , & 12 \\
341 & 682 & = & 16 & , & 11 \\
342 & 684 & = & 17 & , & 10 \\
343 & 686 & = & 18 & , & 9 \\
344 & 688 & = & 19 & , & 8 \\
345 & 690 & = & 20 & , & 7 \\
346 & 692 & = & 21 & , & 6 \\
347 & 694 & = & 22 & , & 5 \\
348 & 696 & = & 23 & , & 4 \\
349 & 698 & = & 24 & , & 3 \\
350 & 700 & = & 25 & , & 2 \\
351 & 702 & = & 26 & , & 1 \\
352 & 704 & = & 1 & , & 27 \\
353 & 706 & = & 2 & , & 26 \\
354 & 708 & = & 3 & , & 25 \\
355 & 710 & = & 4 & , & 24 \\
356 & 712 & = & 5 & , & 23 \\
357 & 714 & = & 6 & , & 22 \\
358 & 716 & = & 7 & , & 21 \\
359 & 718 & = & 8 & , & 20 \\
360 & 720 & = & 9 & , & 19 \\
361 & 722 & = & 10 & , & 18 \\
362 & 724 & = & 11 & , & 17 \\
363 & 726 & = & 12 & , & 16 \\
364 & 728 & = & 13 & , & 15 \\
365 & 730 & = & 14 & , & 14 \\
366 & 732 & = & 15 & , & 13 \\
367 & 734 & = & 16 & , & 12 \\
368 & 736 & = & 17 & , & 11 \\
369 & 738 & = & 18 & , & 10 \\
370 & 740 & = & 19 & , & 9 \\
371 & 742 & = & 20 & , & 8 \\
372 & 744 & = & 21 & , & 7 \\
373 & 746 & = & 22 & , & 6 \\
374 & 748 & = & 23 & , & 5 \\
375 & 750 & = & 24 & , & 4 \\
376 & 752 & = & 25 & , & 3 \\
377 & 754 & = & 26 & , & 2 \\
378 & 756 & = & 27 & , & 1 \\
379 & 758 & = & 1 & , & 28 \\
380 & 760 & = & 2 & , & 27 \\
381 & 762 & = & 3 & , & 26 \\
382 & 764 & = & 4 & , & 25 \\
383 & 766 & = & 5 & , & 24 \\
384 & 768 & = & 6 & , & 23 \\
385 & 770 & = & 7 & , & 22 \\
386 & 772 & = & 8 & , & 21 \\
387 & 774 & = & 9 & , & 20 \\
388 & 776 & = & 10 & , & 19 \\
389 & 778 & = & 11 & , & 18 \\
390 & 780 & = & 12 & , & 17 \\
391 & 782 & = & 13 & , & 16 \\
392 & 784 & = & 14 & , & 15 \\
393 & 786 & = & 15 & , & 14 \\
394 & 788 & = & 16 & , & 13 \\
395 & 790 & = & 17 & , & 12 \\
396 & 792 & = & 18 & , & 11 \\
397 & 794 & = & 19 & , & 10 \\
398 & 796 & = & 20 & , & 9 \\
399 & 798 & = & 21 & , & 8 \\
400 & 800 & = & 22 & , & 7 \\
401 & 802 & = & 23 & , & 6 \\
402 & 804 & = & 24 & , & 5 \\
403 & 806 & = & 25 & , & 4 \\
404 & 808 & = & 26 & , & 3 \\
405 & 810 & = & 27 & , & 2 \\
406 & 812 & = & 28 & , & 1 \\
407 & 814 & = & 1 & , & 29 \\
408 & 816 & = & 2 & , & 28 \\
409 & 818 & = & 3 & , & 27 \\
410 & 820 & = & 4 & , & 26 \\
411 & 822 & = & 5 & , & 25 \\
412 & 824 & = & 6 & , & 24 \\
413 & 826 & = & 7 & , & 23 \\
414 & 828 & = & 8 & , & 22 \\
415 & 830 & = & 9 & , & 21 \\
416 & 832 & = & 10 & , & 20 \\
417 & 834 & = & 11 & , & 19 \\
418 & 836 & = & 12 & , & 18 \\
419 & 838 & = & 13 & , & 17 \\
420 & 840 & = & 14 & , & 16 \\
421 & 842 & = & 15 & , & 15 \\
422 & 844 & = & 16 & , & 14 \\
423 & 846 & = & 17 & , & 13 \\
424 & 848 & = & 18 & , & 12 \\
425 & 850 & = & 19 & , & 11 \\
426 & 852 & = & 20 & , & 10 \\
427 & 854 & = & 21 & , & 9 \\
428 & 856 & = & 22 & , & 8 \\
429 & 858 & = & 23 & , & 7 \\
430 & 860 & = & 24 & , & 6 \\
431 & 862 & = & 25 & , & 5 \\
432 & 864 & = & 26 & , & 4 \\
433 & 866 & = & 27 & , & 3 \\
434 & 868 & = & 28 & , & 2 \\
435 & 870 & = & 29 & , & 1 \\
436 & 872 & = & 1 & , & 30 \\
437 & 874 & = & 2 & , & 29 \\
438 & 876 & = & 3 & , & 28 \\
439 & 878 & = & 4 & , & 27 \\
440 & 880 & = & 5 & , & 26 \\
441 & 882 & = & 6 & , & 25 \\
442 & 884 & = & 7 & , & 24 \\
443 & 886 & = & 8 & , & 23 \\
444 & 888 & = & 9 & , & 22 \\
445 & 890 & = & 10 & , & 21 \\
446 & 892 & = & 11 & , & 20 \\
447 & 894 & = & 12 & , & 19 \\
448 & 896 & = & 13 & , & 18 \\
449 & 898 & = & 14 & , & 17 \\
450 & 900 & = & 15 & , & 16 \\
451 & 902 & = & 16 & , & 15 \\
452 & 904 & = & 17 & , & 14 \\
453 & 906 & = & 18 & , & 13 \\
454 & 908 & = & 19 & , & 12 \\
455 & 910 & = & 20 & , & 11 \\
456 & 912 & = & 21 & , & 10 \\
457 & 914 & = & 22 & , & 9 \\
458 & 916 & = & 23 & , & 8 \\
459 & 918 & = & 24 & , & 7 \\
460 & 920 & = & 25 & , & 6 \\
461 & 922 & = & 26 & , & 5 \\
462 & 924 & = & 27 & , & 4 \\
463 & 926 & = & 28 & , & 3 \\
464 & 928 & = & 29 & , & 2 \\
465 & 930 & = & 30 & , & 1 \\
466 & 932 & = & 1 & , & 31 \\
467 & 934 & = & 2 & , & 30 \\
468 & 936 & = & 3 & , & 29 \\
469 & 938 & = & 4 & , & 28 \\
470 & 940 & = & 5 & , & 27 \\
471 & 942 & = & 6 & , & 26 \\
472 & 944 & = & 7 & , & 25 \\
473 & 946 & = & 8 & , & 24 \\
474 & 948 & = & 9 & , & 23 \\
475 & 950 & = & 10 & , & 22 \\
476 & 952 & = & 11 & , & 21 \\
477 & 954 & = & 12 & , & 20 \\
478 & 956 & = & 13 & , & 19 \\
479 & 958 & = & 14 & , & 18 \\
480 & 960 & = & 15 & , & 17 \\
481 & 962 & = & 16 & , & 16 \\
482 & 964 & = & 17 & , & 15 \\
483 & 966 & = & 18 & , & 14 \\
484 & 968 & = & 19 & , & 13 \\
485 & 970 & = & 20 & , & 12 \\
486 & 972 & = & 21 & , & 11 \\
487 & 974 & = & 22 & , & 10 \\
488 & 976 & = & 23 & , & 9 \\
489 & 978 & = & 24 & , & 8 \\
490 & 980 & = & 25 & , & 7 \\
491 & 982 & = & 26 & , & 6 \\
492 & 984 & = & 27 & , & 5 \\
493 & 986 & = & 28 & , & 4 \\
494 & 988 & = & 29 & , & 3 \\
495 & 990 & = & 30 & , & 2 \\
496 & 992 & = & 31 & , & 1 \\
497 & 994 & = & 1 & , & 32 \\
498 & 996 & = & 2 & , & 31 \\
499 & 998 & = & 3 & , & 30 \\
500 & 1000 & = & 4 & , & 29 \\
501 & 1002 & = & 5 & , & 28 \\
502 & 1004 & = & 6 & , & 27 \\
503 & 1006 & = & 7 & , & 26 \\
504 & 1008 & = & 8 & , & 25 \\
505 & 1010 & = & 9 & , & 24 \\
506 & 1012 & = & 10 & , & 23 \\
507 & 1014 & = & 11 & , & 22 \\
508 & 1016 & = & 12 & , & 21 \\
509 & 1018 & = & 13 & , & 20 \\
510 & 1020 & = & 14 & , & 19 \\
511 & 1022 & = & 15 & , & 18 \\
512 & 1024 & = & 16 & , & 17 \\
513 & 1026 & = & 17 & , & 16 \\
514 & 1028 & = & 18 & , & 15 \\
515 & 1030 & = & 19 & , & 14 \\
516 & 1032 & = & 20 & , & 13 \\
517 & 1034 & = & 21 & , & 12 \\
518 & 1036 & = & 22 & , & 11 \\
519 & 1038 & = & 23 & , & 10 \\
520 & 1040 & = & 24 & , & 9 \\
521 & 1042 & = & 25 & , & 8 \\
522 & 1044 & = & 26 & , & 7 \\
523 & 1046 & = & 27 & , & 6 \\
524 & 1048 & = & 28 & , & 5 \\
525 & 1050 & = & 29 & , & 4 \\
526 & 1052 & = & 30 & , & 3 \\
527 & 1054 & = & 31 & , & 2 \\
528 & 1056 & = & 32 & , & 1 \\
529 & 1058 & = & 1 & , & 33 \\
530 & 1060 & = & 2 & , & 32 \\
531 & 1062 & = & 3 & , & 31 \\
532 & 1064 & = & 4 & , & 30 \\
533 & 1066 & = & 5 & , & 29 \\
534 & 1068 & = & 6 & , & 28 \\
535 & 1070 & = & 7 & , & 27 \\
536 & 1072 & = & 8 & , & 26 \\
537 & 1074 & = & 9 & , & 25 \\
538 & 1076 & = & 10 & , & 24 \\
539 & 1078 & = & 11 & , & 23 \\
540 & 1080 & = & 12 & , & 22 \\
541 & 1082 & = & 13 & , & 21 \\
542 & 1084 & = & 14 & , & 20 \\
543 & 1086 & = & 15 & , & 19 \\
544 & 1088 & = & 16 & , & 18 \\
545 & 1090 & = & 17 & , & 17 \\
546 & 1092 & = & 18 & , & 16 \\
547 & 1094 & = & 19 & , & 15 \\
548 & 1096 & = & 20 & , & 14 \\
549 & 1098 & = & 21 & , & 13 \\
550 & 1100 & = & 22 & , & 12 \\
551 & 1102 & = & 23 & , & 11 \\
552 & 1104 & = & 24 & , & 10 \\
553 & 1106 & = & 25 & , & 9 \\
554 & 1108 & = & 26 & , & 8 \\
555 & 1110 & = & 27 & , & 7 \\
556 & 1112 & = & 28 & , & 6 \\
557 & 1114 & = & 29 & , & 5 \\
558 & 1116 & = & 30 & , & 4 \\
559 & 1118 & = & 31 & , & 3 \\
560 & 1120 & = & 32 & , & 2 \\
561 & 1122 & = & 33 & , & 1 \\
562 & 1124 & = & 1 & , & 34 \\
563 & 1126 & = & 2 & , & 33 \\
564 & 1128 & = & 3 & , & 32 \\
565 & 1130 & = & 4 & , & 31 \\
566 & 1132 & = & 5 & , & 30 \\
567 & 1134 & = & 6 & , & 29 \\
568 & 1136 & = & 7 & , & 28 \\
569 & 1138 & = & 8 & , & 27 \\
570 & 1140 & = & 9 & , & 26 \\
571 & 1142 & = & 10 & , & 25 \\
572 & 1144 & = & 11 & , & 24 \\
573 & 1146 & = & 12 & , & 23 \\
574 & 1148 & = & 13 & , & 22 \\
575 & 1150 & = & 14 & , & 21 \\
576 & 1152 & = & 15 & , & 20 \\
577 & 1154 & = & 16 & , & 19 \\
578 & 1156 & = & 17 & , & 18 \\
579 & 1158 & = & 18 & , & 17 \\
580 & 1160 & = & 19 & , & 16 \\
581 & 1162 & = & 20 & , & 15 \\
582 & 1164 & = & 21 & , & 14 \\
583 & 1166 & = & 22 & , & 13 \\
584 & 1168 & = & 23 & , & 12 \\
585 & 1170 & = & 24 & , & 11 \\
586 & 1172 & = & 25 & , & 10 \\
587 & 1174 & = & 26 & , & 9 \\
588 & 1176 & = & 27 & , & 8 \\
589 & 1178 & = & 28 & , & 7 \\
590 & 1180 & = & 29 & , & 6 \\
591 & 1182 & = & 30 & , & 5 \\
592 & 1184 & = & 31 & , & 4 \\
593 & 1186 & = & 32 & , & 3 \\
594 & 1188 & = & 33 & , & 2 \\
595 & 1190 & = & 34 & , & 1 \\
596 & 1192 & = & 1 & , & 35 \\
597 & 1194 & = & 2 & , & 34 \\
598 & 1196 & = & 3 & , & 33 \\
599 & 1198 & = & 4 & , & 32 \\
600 & 1200 & = & 5 & , & 31 \\
601 & 1202 & = & 6 & , & 30 \\
602 & 1204 & = & 7 & , & 29 \\
603 & 1206 & = & 8 & , & 28 \\
604 & 1208 & = & 9 & , & 27 \\
605 & 1210 & = & 10 & , & 26 \\
606 & 1212 & = & 11 & , & 25 \\
607 & 1214 & = & 12 & , & 24 \\
608 & 1216 & = & 13 & , & 23 \\
609 & 1218 & = & 14 & , & 22 \\
610 & 1220 & = & 15 & , & 21 \\
611 & 1222 & = & 16 & , & 20 \\
612 & 1224 & = & 17 & , & 19 \\
613 & 1226 & = & 18 & , & 18 \\
614 & 1228 & = & 19 & , & 17 \\
615 & 1230 & = & 20 & , & 16 \\
616 & 1232 & = & 21 & , & 15 \\
617 & 1234 & = & 22 & , & 14 \\
618 & 1236 & = & 23 & , & 13 \\
619 & 1238 & = & 24 & , & 12 \\
620 & 1240 & = & 25 & , & 11 \\
621 & 1242 & = & 26 & , & 10 \\
622 & 1244 & = & 27 & , & 9 \\
623 & 1246 & = & 28 & , & 8 \\
624 & 1248 & = & 29 & , & 7 \\
625 & 1250 & = & 30 & , & 6 \\
626 & 1252 & = & 31 & , & 5 \\
627 & 1254 & = & 32 & , & 4 \\
628 & 1256 & = & 33 & , & 3 \\
629 & 1258 & = & 34 & , & 2 \\
630 & 1260 & = & 35 & , & 1 \\
631 & 1262 & = & 1 & , & 36 \\
632 & 1264 & = & 2 & , & 35 \\
633 & 1266 & = & 3 & , & 34 \\
634 & 1268 & = & 4 & , & 33 \\
635 & 1270 & = & 5 & , & 32 \\
636 & 1272 & = & 6 & , & 31 \\
637 & 1274 & = & 7 & , & 30 \\
638 & 1276 & = & 8 & , & 29 \\
639 & 1278 & = & 9 & , & 28 \\
640 & 1280 & = & 10 & , & 27 \\
641 & 1282 & = & 11 & , & 26 \\
642 & 1284 & = & 12 & , & 25 \\
643 & 1286 & = & 13 & , & 24 \\
644 & 1288 & = & 14 & , & 23 \\
645 & 1290 & = & 15 & , & 22 \\
646 & 1292 & = & 16 & , & 21 \\
647 & 1294 & = & 17 & , & 20 \\
648 & 1296 & = & 18 & , & 19 \\
649 & 1298 & = & 19 & , & 18 \\
650 & 1300 & = & 20 & , & 17 \\
651 & 1302 & = & 21 & , & 16 \\
652 & 1304 & = & 22 & , & 15 \\
653 & 1306 & = & 23 & , & 14 \\
654 & 1308 & = & 24 & , & 13 \\
655 & 1310 & = & 25 & , & 12 \\
656 & 1312 & = & 26 & , & 11 \\
657 & 1314 & = & 27 & , & 10 \\
658 & 1316 & = & 28 & , & 9 \\
659 & 1318 & = & 29 & , & 8 \\
660 & 1320 & = & 30 & , & 7 \\
661 & 1322 & = & 31 & , & 6 \\
662 & 1324 & = & 32 & , & 5 \\
663 & 1326 & = & 33 & , & 4 \\
664 & 1328 & = & 34 & , & 3 \\
665 & 1330 & = & 35 & , & 2 \\
666 & 1332 & = & 36 & , & 1 \\
667 & 1334 & = & 1 & , & 37 \\
668 & 1336 & = & 2 & , & 36 \\
669 & 1338 & = & 3 & , & 35 \\
670 & 1340 & = & 4 & , & 34 \\
671 & 1342 & = & 5 & , & 33 \\
672 & 1344 & = & 6 & , & 32 \\
673 & 1346 & = & 7 & , & 31 \\
674 & 1348 & = & 8 & , & 30 \\
675 & 1350 & = & 9 & , & 29 \\
676 & 1352 & = & 10 & , & 28 \\
677 & 1354 & = & 11 & , & 27 \\
678 & 1356 & = & 12 & , & 26 \\
679 & 1358 & = & 13 & , & 25 \\
680 & 1360 & = & 14 & , & 24 \\
681 & 1362 & = & 15 & , & 23 \\
682 & 1364 & = & 16 & , & 22 \\
683 & 1366 & = & 17 & , & 21 \\
684 & 1368 & = & 18 & , & 20 \\
685 & 1370 & = & 19 & , & 19 \\
686 & 1372 & = & 20 & , & 18 \\
687 & 1374 & = & 21 & , & 17 \\
688 & 1376 & = & 22 & , & 16 \\
689 & 1378 & = & 23 & , & 15 \\
690 & 1380 & = & 24 & , & 14 \\
691 & 1382 & = & 25 & , & 13 \\
692 & 1384 & = & 26 & , & 12 \\
693 & 1386 & = & 27 & , & 11 \\
694 & 1388 & = & 28 & , & 10 \\
695 & 1390 & = & 29 & , & 9 \\
696 & 1392 & = & 30 & , & 8 \\
697 & 1394 & = & 31 & , & 7 \\
698 & 1396 & = & 32 & , & 6 \\
699 & 1398 & = & 33 & , & 5 \\
700 & 1400 & = & 34 & , & 4 \\
701 & 1402 & = & 35 & , & 3 \\
702 & 1404 & = & 36 & , & 2 \\
703 & 1406 & = & 37 & , & 1 \\
704 & 1408 & = & 1 & , & 38 \\
705 & 1410 & = & 2 & , & 37 \\
706 & 1412 & = & 3 & , & 36 \\
707 & 1414 & = & 4 & , & 35 \\
708 & 1416 & = & 5 & , & 34 \\
709 & 1418 & = & 6 & , & 33 \\
710 & 1420 & = & 7 & , & 32 \\
711 & 1422 & = & 8 & , & 31 \\
712 & 1424 & = & 9 & , & 30 \\
713 & 1426 & = & 10 & , & 29 \\
714 & 1428 & = & 11 & , & 28 \\
715 & 1430 & = & 12 & , & 27 \\
716 & 1432 & = & 13 & , & 26 \\
717 & 1434 & = & 14 & , & 25 \\
718 & 1436 & = & 15 & , & 24 \\
719 & 1438 & = & 16 & , & 23 \\
720 & 1440 & = & 17 & , & 22 \\
721 & 1442 & = & 18 & , & 21 \\
722 & 1444 & = & 19 & , & 20 \\
723 & 1446 & = & 20 & , & 19 \\
724 & 1448 & = & 21 & , & 18 \\
725 & 1450 & = & 22 & , & 17 \\
726 & 1452 & = & 23 & , & 16 \\
727 & 1454 & = & 24 & , & 15 \\
728 & 1456 & = & 25 & , & 14 \\
729 & 1458 & = & 26 & , & 13 \\
730 & 1460 & = & 27 & , & 12 \\
731 & 1462 & = & 28 & , & 11 \\
732 & 1464 & = & 29 & , & 10 \\
733 & 1466 & = & 30 & , & 9 \\
734 & 1468 & = & 31 & , & 8 \\
735 & 1470 & = & 32 & , & 7 \\
736 & 1472 & = & 33 & , & 6 \\
737 & 1474 & = & 34 & , & 5 \\
738 & 1476 & = & 35 & , & 4 \\
739 & 1478 & = & 36 & , & 3 \\
740 & 1480 & = & 37 & , & 2 \\
741 & 1482 & = & 38 & , & 1 \\
742 & 1484 & = & 1 & , & 39 \\
743 & 1486 & = & 2 & , & 38 \\
744 & 1488 & = & 3 & , & 37 \\
745 & 1490 & = & 4 & , & 36 \\
746 & 1492 & = & 5 & , & 35 \\
747 & 1494 & = & 6 & , & 34 \\
748 & 1496 & = & 7 & , & 33 \\
749 & 1498 & = & 8 & , & 32 \\
750 & 1500 & = & 9 & , & 31 \\
751 & 1502 & = & 10 & , & 30 \\
752 & 1504 & = & 11 & , & 29 \\
753 & 1506 & = & 12 & , & 28 \\
754 & 1508 & = & 13 & , & 27 \\
755 & 1510 & = & 14 & , & 26 \\
756 & 1512 & = & 15 & , & 25 \\
757 & 1514 & = & 16 & , & 24 \\
758 & 1516 & = & 17 & , & 23 \\
759 & 1518 & = & 18 & , & 22 \\
760 & 1520 & = & 19 & , & 21 \\
761 & 1522 & = & 20 & , & 20 \\
762 & 1524 & = & 21 & , & 19 \\
763 & 1526 & = & 22 & , & 18 \\
764 & 1528 & = & 23 & , & 17 \\
765 & 1530 & = & 24 & , & 16 \\
766 & 1532 & = & 25 & , & 15 \\
767 & 1534 & = & 26 & , & 14 \\
768 & 1536 & = & 27 & , & 13 \\
769 & 1538 & = & 28 & , & 12 \\
770 & 1540 & = & 29 & , & 11 \\
771 & 1542 & = & 30 & , & 10 \\
772 & 1544 & = & 31 & , & 9 \\
773 & 1546 & = & 32 & , & 8 \\
774 & 1548 & = & 33 & , & 7 \\
775 & 1550 & = & 34 & , & 6 \\
776 & 1552 & = & 35 & , & 5 \\
777 & 1554 & = & 36 & , & 4 \\
778 & 1556 & = & 37 & , & 3 \\
779 & 1558 & = & 38 & , & 2 \\
780 & 1560 & = & 39 & , & 1 \\
781 & 1562 & = & 1 & , & 40 \\
782 & 1564 & = & 2 & , & 39 \\
783 & 1566 & = & 3 & , & 38 \\
784 & 1568 & = & 4 & , & 37 \\
785 & 1570 & = & 5 & , & 36 \\
786 & 1572 & = & 6 & , & 35 \\
787 & 1574 & = & 7 & , & 34 \\
788 & 1576 & = & 8 & , & 33 \\
789 & 1578 & = & 9 & , & 32 \\
790 & 1580 & = & 10 & , & 31 \\
791 & 1582 & = & 11 & , & 30 \\
792 & 1584 & = & 12 & , & 29 \\
793 & 1586 & = & 13 & , & 28 \\
794 & 1588 & = & 14 & , & 27 \\
795 & 1590 & = & 15 & , & 26 \\
796 & 1592 & = & 16 & , & 25 \\
797 & 1594 & = & 17 & , & 24 \\
798 & 1596 & = & 18 & , & 23 \\
799 & 1598 & = & 19 & , & 22 \\
800 & 1600 & = & 20 & , & 21 \\
801 & 1602 & = & 21 & , & 20 \\
802 & 1604 & = & 22 & , & 19 \\
803 & 1606 & = & 23 & , & 18 \\
804 & 1608 & = & 24 & , & 17 \\
805 & 1610 & = & 25 & , & 16 \\
806 & 1612 & = & 26 & , & 15 \\
807 & 1614 & = & 27 & , & 14 \\
808 & 1616 & = & 28 & , & 13 \\
809 & 1618 & = & 29 & , & 12 \\
810 & 1620 & = & 30 & , & 11 \\
811 & 1622 & = & 31 & , & 10 \\
812 & 1624 & = & 32 & , & 9 \\
813 & 1626 & = & 33 & , & 8 \\
814 & 1628 & = & 34 & , & 7 \\
815 & 1630 & = & 35 & , & 6 \\
816 & 1632 & = & 36 & , & 5 \\
817 & 1634 & = & 37 & , & 4 \\
818 & 1636 & = & 38 & , & 3 \\
819 & 1638 & = & 39 & , & 2 \\
820 & 1640 & = & 40 & , & 1 \\
821 & 1642 & = & 1 & , & 41 \\
822 & 1644 & = & 2 & , & 40 \\
823 & 1646 & = & 3 & , & 39 \\
824 & 1648 & = & 4 & , & 38 \\
825 & 1650 & = & 5 & , & 37 \\
826 & 1652 & = & 6 & , & 36 \\
827 & 1654 & = & 7 & , & 35 \\
828 & 1656 & = & 8 & , & 34 \\
829 & 1658 & = & 9 & , & 33 \\
830 & 1660 & = & 10 & , & 32 \\
831 & 1662 & = & 11 & , & 31 \\
832 & 1664 & = & 12 & , & 30 \\
833 & 1666 & = & 13 & , & 29 \\
834 & 1668 & = & 14 & , & 28 \\
835 & 1670 & = & 15 & , & 27 \\
836 & 1672 & = & 16 & , & 26 \\
837 & 1674 & = & 17 & , & 25 \\
838 & 1676 & = & 18 & , & 24 \\
839 & 1678 & = & 19 & , & 23 \\
840 & 1680 & = & 20 & , & 22 \\
841 & 1682 & = & 21 & , & 21 \\
842 & 1684 & = & 22 & , & 20 \\
843 & 1686 & = & 23 & , & 19 \\
844 & 1688 & = & 24 & , & 18 \\
845 & 1690 & = & 25 & , & 17 \\
846 & 1692 & = & 26 & , & 16 \\
847 & 1694 & = & 27 & , & 15 \\
848 & 1696 & = & 28 & , & 14 \\
849 & 1698 & = & 29 & , & 13 \\
850 & 1700 & = & 30 & , & 12 \\
851 & 1702 & = & 31 & , & 11 \\
852 & 1704 & = & 32 & , & 10 \\
853 & 1706 & = & 33 & , & 9 \\
854 & 1708 & = & 34 & , & 8 \\
855 & 1710 & = & 35 & , & 7 \\
856 & 1712 & = & 36 & , & 6 \\
857 & 1714 & = & 37 & , & 5 \\
858 & 1716 & = & 38 & , & 4 \\
859 & 1718 & = & 39 & , & 3 \\
860 & 1720 & = & 40 & , & 2 \\
861 & 1722 & = & 41 & , & 1 \\
862 & 1724 & = & 1 & , & 42 \\
863 & 1726 & = & 2 & , & 41 \\
864 & 1728 & = & 3 & , & 40 \\
865 & 1730 & = & 4 & , & 39 \\
866 & 1732 & = & 5 & , & 38 \\
867 & 1734 & = & 6 & , & 37 \\
868 & 1736 & = & 7 & , & 36 \\
869 & 1738 & = & 8 & , & 35 \\
870 & 1740 & = & 9 & , & 34 \\
871 & 1742 & = & 10 & , & 33 \\
872 & 1744 & = & 11 & , & 32 \\
873 & 1746 & = & 12 & , & 31 \\
874 & 1748 & = & 13 & , & 30 \\
875 & 1750 & = & 14 & , & 29 \\
876 & 1752 & = & 15 & , & 28 \\
877 & 1754 & = & 16 & , & 27 \\
878 & 1756 & = & 17 & , & 26 \\
879 & 1758 & = & 18 & , & 25 \\
880 & 1760 & = & 19 & , & 24 \\
881 & 1762 & = & 20 & , & 23 \\
882 & 1764 & = & 21 & , & 22 \\
883 & 1766 & = & 22 & , & 21 \\
884 & 1768 & = & 23 & , & 20 \\
885 & 1770 & = & 24 & , & 19 \\
886 & 1772 & = & 25 & , & 18 \\
887 & 1774 & = & 26 & , & 17 \\
888 & 1776 & = & 27 & , & 16 \\
889 & 1778 & = & 28 & , & 15 \\
890 & 1780 & = & 29 & , & 14 \\
891 & 1782 & = & 30 & , & 13 \\
892 & 1784 & = & 31 & , & 12 \\
893 & 1786 & = & 32 & , & 11 \\
894 & 1788 & = & 33 & , & 10 \\
895 & 1790 & = & 34 & , & 9 \\
896 & 1792 & = & 35 & , & 8 \\
897 & 1794 & = & 36 & , & 7 \\
898 & 1796 & = & 37 & , & 6 \\
899 & 1798 & = & 38 & , & 5 \\
900 & 1800 & = & 39 & , & 4 \\
901 & 1802 & = & 40 & , & 3 \\
902 & 1804 & = & 41 & , & 2 \\
903 & 1806 & = & 42 & , & 1 \\
904 & 1808 & = & 1 & , & 43 \\
905 & 1810 & = & 2 & , & 42 \\
906 & 1812 & = & 3 & , & 41 \\
907 & 1814 & = & 4 & , & 40 \\
908 & 1816 & = & 5 & , & 39 \\
909 & 1818 & = & 6 & , & 38 \\
910 & 1820 & = & 7 & , & 37 \\
911 & 1822 & = & 8 & , & 36 \\
912 & 1824 & = & 9 & , & 35 \\
913 & 1826 & = & 10 & , & 34 \\
914 & 1828 & = & 11 & , & 33 \\
915 & 1830 & = & 12 & , & 32 \\
916 & 1832 & = & 13 & , & 31 \\
917 & 1834 & = & 14 & , & 30 \\
918 & 1836 & = & 15 & , & 29 \\
919 & 1838 & = & 16 & , & 28 \\
920 & 1840 & = & 17 & , & 27 \\
921 & 1842 & = & 18 & , & 26 \\
922 & 1844 & = & 19 & , & 25 \\
923 & 1846 & = & 20 & , & 24 \\
924 & 1848 & = & 21 & , & 23 \\
925 & 1850 & = & 22 & , & 22 \\
926 & 1852 & = & 23 & , & 21 \\
927 & 1854 & = & 24 & , & 20 \\
928 & 1856 & = & 25 & , & 19 \\
929 & 1858 & = & 26 & , & 18 \\
930 & 1860 & = & 27 & , & 17 \\
931 & 1862 & = & 28 & , & 16 \\
932 & 1864 & = & 29 & , & 15 \\
933 & 1866 & = & 30 & , & 14 \\
934 & 1868 & = & 31 & , & 13 \\
935 & 1870 & = & 32 & , & 12 \\
936 & 1872 & = & 33 & , & 11 \\
937 & 1874 & = & 34 & , & 10 \\
938 & 1876 & = & 35 & , & 9 \\
939 & 1878 & = & 36 & , & 8 \\
940 & 1880 & = & 37 & , & 7 \\
941 & 1882 & = & 38 & , & 6 \\
942 & 1884 & = & 39 & , & 5 \\
943 & 1886 & = & 40 & , & 4 \\
944 & 1888 & = & 41 & , & 3 \\
945 & 1890 & = & 42 & , & 2 \\
946 & 1892 & = & 43 & , & 1 \\
947 & 1894 & = & 1 & , & 44 \\
948 & 1896 & = & 2 & , & 43 \\
949 & 1898 & = & 3 & , & 42 \\
950 & 1900 & = & 4 & , & 41 \\
951 & 1902 & = & 5 & , & 40 \\
952 & 1904 & = & 6 & , & 39 \\
953 & 1906 & = & 7 & , & 38 \\
954 & 1908 & = & 8 & , & 37 \\
955 & 1910 & = & 9 & , & 36 \\
956 & 1912 & = & 10 & , & 35 \\
957 & 1914 & = & 11 & , & 34 \\
958 & 1916 & = & 12 & , & 33 \\
959 & 1918 & = & 13 & , & 32 \\
960 & 1920 & = & 14 & , & 31 \\
961 & 1922 & = & 15 & , & 30 \\
962 & 1924 & = & 16 & , & 29 \\
963 & 1926 & = & 17 & , & 28 \\
964 & 1928 & = & 18 & , & 27 \\
965 & 1930 & = & 19 & , & 26 \\
966 & 1932 & = & 20 & , & 25 \\
967 & 1934 & = & 21 & , & 24 \\
968 & 1936 & = & 22 & , & 23 \\
969 & 1938 & = & 23 & , & 22 \\
970 & 1940 & = & 24 & , & 21 \\
971 & 1942 & = & 25 & , & 20 \\
972 & 1944 & = & 26 & , & 19 \\
973 & 1946 & = & 27 & , & 18 \\
974 & 1948 & = & 28 & , & 17 \\
975 & 1950 & = & 29 & , & 16 \\
976 & 1952 & = & 30 & , & 15 \\
977 & 1954 & = & 31 & , & 14 \\
978 & 1956 & = & 32 & , & 13 \\
979 & 1958 & = & 33 & , & 12 \\
980 & 1960 & = & 34 & , & 11 \\
981 & 1962 & = & 35 & , & 10 \\
982 & 1964 & = & 36 & , & 9 \\
983 & 1966 & = & 37 & , & 8 \\
984 & 1968 & = & 38 & , & 7 \\
985 & 1970 & = & 39 & , & 6 \\
986 & 1972 & = & 40 & , & 5 \\
987 & 1974 & = & 41 & , & 4 \\
988 & 1976 & = & 42 & , & 3 \\
989 & 1978 & = & 43 & , & 2 \\
990 & 1980 & = & 44 & , & 1 \\
991 & 1982 & = & 1 & , & 45 \\
992 & 1984 & = & 2 & , & 44 \\
993 & 1986 & = & 3 & , & 43 \\
994 & 1988 & = & 4 & , & 42 \\
995 & 1990 & = & 5 & , & 41 \\
996 & 1992 & = & 6 & , & 40 \\
997 & 1994 & = & 7 & , & 39 \\
998 & 1996 & = & 8 & , & 38 \\
999 & 1998 & = & 9 & , & 37 \\
1000 & 2000 & = & 10 & , & 36 \\
1001 & 2002 & = & 11 & , & 35 \\
1002 & 2004 & = & 12 & , & 34 \\
1003 & 2006 & = & 13 & , & 33 \\
1004 & 2008 & = & 14 & , & 32 \\
1005 & 2010 & = & 15 & , & 31 \\
1006 & 2012 & = & 16 & , & 30 \\
1007 & 2014 & = & 17 & , & 29 \\
1008 & 2016 & = & 18 & , & 28 \\
1009 & 2018 & = & 19 & , & 27 \\
1010 & 2020 & = & 20 & , & 26 \\
1011 & 2022 & = & 21 & , & 25 \\
1012 & 2024 & = & 22 & , & 24 \\
1013 & 2026 & = & 23 & , & 23 \\
1014 & 2028 & = & 24 & , & 22 \\
1015 & 2030 & = & 25 & , & 21 \\
1016 & 2032 & = & 26 & , & 20 \\
1017 & 2034 & = & 27 & , & 19 \\
1018 & 2036 & = & 28 & , & 18 \\
1019 & 2038 & = & 29 & , & 17 \\
1020 & 2040 & = & 30 & , & 16 \\
1021 & 2042 & = & 31 & , & 15 \\
1022 & 2044 & = & 32 & , & 14 \\
1023 & 2046 & = & 33 & , & 13 \\
1024 & 2048 & = & 34 & , & 12 \\
1025 & 2050 & = & 35 & , & 11 \\
1026 & 2052 & = & 36 & , & 10 \\
1027 & 2054 & = & 37 & , & 9 \\
1028 & 2056 & = & 38 & , & 8 \\
1029 & 2058 & = & 39 & , & 7 \\
1030 & 2060 & = & 40 & , & 6 \\
1031 & 2062 & = & 41 & , & 5 \\
1032 & 2064 & = & 42 & , & 4 \\
1033 & 2066 & = & 43 & , & 3 \\
1034 & 2068 & = & 44 & , & 2 \\
1035 & 2070 & = & 45 & , & 1 \\
\end{array}\)\)
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
 楼主| 发表于 2020-6-26 15:12:53 | 显示全部楼层
本帖最后由 王守恩 于 2020-6-26 20:10 编辑
dlpg070 发表于 2020-6-9 09:45
2020= 20,26

代码如下


由 1 形成的 “大” 的交错排列有1种:1。
由 12 形成的 “大小” 的交错排列有1种:21。
由 123 形成的 “大小大” 的交错排列有2种:213,312。
由 1234 形成的 “大小大小” 的交错排列有5种:2143,3142,3241,4132,4231。
由 12345 形成的 “大小大小大” 的交错排列有16种:21435,21534,31425,31524,32415,32514,41325,41523,42315,42513,43512,51324,51423,52314,52413,53412。
1,1,2,5,16,61,.....,有好的通项公式吗?
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
 楼主| 发表于 2020-6-27 08:27:34 | 显示全部楼层
本帖最后由 王守恩 于 2020-6-27 08:45 编辑
王守恩 发表于 2020-6-26 15:12
由 1 形成的 “大” 的交错排列有1种:1。
由 12 形成的 “大小” 的交错排列有1种:21。
由 123 形 ...


\(\D a(n)=\bigg[2\ n!\ \bigg(\frac{2}{\pi}\bigg)^{n + 1}\bigg]\)
{1, 1, 2, 5, 16, 61, 272, 1385, 7936, 50521, 353791, 2702767,
22368251, 199360995, 1903757268, 19391512295, 209865342434}
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
 楼主| 发表于 2020-7-5 07:28:10 | 显示全部楼层
dlpg070 发表于 2020-6-9 09:45
2020= 20,26

代码如下

       A090681       
1,1,31,5461,3202291,4722116521,14717667114151,86125672563201181,868320396104950823611,
14129659550745551130667441,352552873457246307069012458671,12942188000689093683411117827763301,
675618013651758631167025175564066787331,48743995308245045290420262686473639399176761,......
      Table[(2 EulerE[4 n + 1, 1]), {n, 0, 14}]    这样不更好吗?
{1, 1, 31, 5461, 3202291, 4722116521, 14717667114151, 86125672563201181, 868320396104950823611,
14129659550745551130667441, 352552873457246307069012458671, 12942188000689093683411117827763301,
675618013651758631167025175564066787331, 48743995308245045290420262686473639399176761,
4743959410520839641708579899308953443202738817591}

点评

你的代码能满足你的要求(求出 2020=?,?)吗  发表于 2020-7-5 10:23
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
 楼主| 发表于 2020-7-5 15:26:38 | 显示全部楼层
dlpg070 发表于 2020-6-9 09:45
2020= 20,26

代码如下

您是怎么把(1),(2)粘在一起的,我还是不会。

(1),Table[Range[n], {n, 7}]
{{1}, {1, 2}, {1, 2, 3}, {1, 2, 3, 4}, {1, 2, 3, 4, 5}, {1, 2, 3, 4, 5, 6}}

(2),Table[Range[n, 1, -1], {n, 7}]
{{1}, {2, 1}, {3, 2, 1}, {4, 3, 2, 1}, {5, 4, 3, 2, 1}, {6, 5, 4, 3, 2, 1}}
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2020-7-5 16:42:26 | 显示全部楼层
王守恩 发表于 2020-7-5 15:26
您是怎么把(1),(2)粘在一起的,我还是不会。

(1),Table[Range[n], {n, 7}]

先学会使用<代码>:
1 在编辑窗口上部选择<>
2 把代码复制到代码窗口,也可以直接编写,
3 选择 提交, 即可
  1. (1),Table[Range[n], {n, 7}]
  2. {{1}, {1, 2}, {1, 2, 3}, {1, 2, 3, 4}, {1, 2, 3, 4, 5}, {1, 2, 3, 4, 5, 6}}

  3. (2),Table[Range[n, 1, -1], {n, 7}]
  4. {{1}, {2, 1}, {3, 2, 1}, {4, 3, 2, 1}, {5, 4, 3, 2, 1}, {6, 5, 4, 3, 2, 1}}
复制代码
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2020-7-6 14:38:32 | 显示全部楼层
dlpg070 发表于 2020-7-5 16:42
先学会使用:
1 在编辑窗口上部选择
2 把代码复制到代码窗口,也可以直接编写,

回复王守恩:
由2个基本语句实现2020=?.?的代码
这是一个简单问题,适合做演示,这是初学者与初学者的对话,高手莫笑
你的编码水平进快,有年轻朋友帮助吗?
下面一起讨论,以你的代码为基础,如何如何实现 2020=?,?  
----------------
  1. (*  演示 2020 = ?.? 格式输出
  2. *)
  3. Clear["Global`*"](*先清理内存是个好习惯,想利用以前单元的变量和函数例外*)
  4. len = 45;(*45;   调试时 7 ,正式:45 以下4行可以用";"不显示*)
  5. blist = Table[Range[n], {n, len}](*命名 变量名长度适中,简单有意义,尾部的";"表示不显示
  6.        (1),Table[Range[n],{n,7}]          *)
  7. blist = blist // Flatten(*压平,去掉内部{},为演示与前行分开*)
  8. clist = Table[Range[n, 1, -1], {n, len}] (*命名
  9.        (2),Table[Range[n,1,-1],{n,7}] *)
  10. clist = clist // Flatten(*压平,去掉内部{},为演示与前行分开*)

  11. out = Table[{n, 2*n, "=", blist[[n]], ",", clist[[n]]}, {n, 1,
  12.    Length[blist]}];(*生成格式化数据*)
  13. Grid[out, Alignment -> Left](*显示格式化数据,左对齐 *)
复制代码
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
 楼主| 发表于 2020-9-29 16:41:33 | 显示全部楼层
dlpg070 发表于 2020-7-6 14:38
回复王守恩:
由2个基本语句实现2020=?.?的代码
这是一个简单问题,适合做演示,这是初学者与初学者的对话 ...

\(\D a_n=\bigg\lfloor\sum_{k= 0}^n\frac{3^k*k!}{(k+1)^k}\bigg\rfloor\)

1, 2, 4, 7, 10, 13, 18, 23, 29, 36, 45, 54, 65, 78, 92, 108, 127, 148, 172,
198, 229, 263, 302, 346, 395, 451, 513, 583, 662, 751, 850, 961, 1086, 1225,
1382, 1556, 1752, 1971, 2216, 2489, 2795, 3136, 3517, 3943, .........................

点评

通项及计算都对,OEIS没有收录,有什么特点?  发表于 2020-9-29 18:08
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
 楼主| 发表于 2020-10-31 17:35:25 | 显示全部楼层
王守恩 发表于 2020-9-29 16:41
\(\D a_n=\bigg\lfloor\sum_{k= 0}^n\frac{3^k*k!}{(k+1)^k}\bigg\rfloor\)

1, 2, 4, 7, 10, 13, 18, ...

\(\D\sum_{k=1}^{\infty}\frac{k^n}{2^k}\)
{1, 2, 6, 26, 150, 1082, 9366, 94586, 1091670, 14174522,
204495126, 3245265146, 56183135190, .....}
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
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