Very interesting problems..

krassi_holmz · 2005-12-28 00:37:14

I can't understand. Thes smallest solution is
{n^2}, n=1
or if n > 1 {i,n^2-i}, n=2.

seerj · 2005-12-28 07:10:11

please, not the smallest solution. Krassi if u made an algorithm we need at least to find the longest circular sequence! [NOT THE SMALLEST] the smallest thing is n, not the solution. If my geek teacher said that a tip is n<50 there is any reason. What I proposed is a particular problem, and the math scientists found this minimum n. There is a conjecture for which does exist a particular n and further it does always exist a circular sequence with this minimum n, but they can't explain why.
But they found this minimum n.
Even if we can't find it, we can try to find the longest circular sequence at least!
I think now it's ok

In faith

Last edited by seerj (2005-12-28 07:12:23)

John E. Franklin · 2005-12-28 11:01:46

Oops, ignore me, I didn't see last two pages of thread.

Last edited by John E. Franklin (2005-12-28 14:04:57)

krassi_holmz · 2005-12-28 11:56:09

But there's infinity long sircular sequence!

krassi_holmz · 2005-12-28 12:02:29

1,3,6,10,15,11,5,4,12,13,23,2,7,9,16,20,29,27,22,14,35
length=21

krassi_holmz · 2005-12-28 13:25:09

1, 3, 6, 10, 15, 11, 5, 4, 12, 13, 23, 2, 7, 9, 16, 20, 29, 27, 22, 14, 35, 21, 28, 8, 31, 18, 38, 26, 30, 19, 17, 32, 24, 25, 39, 42, 58, 63
length=38

krassi_holmz · 2005-12-28 13:29:05

1, 3, 6, 10, 15, 11, 5, 4, 12, 13, 23, 2, 7, 9, 16, 20, 29, 27, 22, 14, 35, 21, 28, 8, 31, 18, 38, 26, 30, 19, 17, 32, 24, 25, 39, 42, 58, 63, 37, 44, 56, 65, 79, 90, 54, 46, 75, 69, 52, 48
length=50

krassi_holmz · 2005-12-28 13:35:15

1, 3, 6, 10, 15, 11, 5, 4, 12, 13, 23, 2, 7, 9, 16, 20, 29, 27, 22, 14, 35, 21, 28, 8, 31, 18, 38, 26, 30, 19, 17, 32, 24, 25, 39, 42, 58, 63, 37, 44, 56, 65, 79, 90, 54, 46, 75, 69, 52, 48, 33, 67, 77, 92, 104, 40, 41, 59, 62, 82, 87, 34, 47, 53, 68, 76, 45, 55
length=68!!!

krassi_holmz · 2005-12-28 13:38:25

This sequences have been maked with krassi_holmz algoritm!
I told you that it won't be bad.

krassi_holmz · 2005-12-28 13:42:34

I though some statistical methods could help understanding the sequences.
But no, the numbers are VERY RANDOM.

Here's a picture, that shows it:

Last edited by krassi_holmz (2005-12-28 14:16:16)

John E. Franklin · 2005-12-28 14:44:06

I thought I would join in the fun!!
1 63 337 192 169 56 88 537 363 478
51 30 114 142 587 197 532 368 161 239
17 152 689 40 744 156 205 524 5 779
121 168 361 39 25 119 77 599 130 654
246 195 705 79 362 214 147 177 223 218
566 275 454 171 153 72 9 187 438 238
387 13 663 237 163 462 267 574 2 23
146 754 87 442 399 330 295 434 466 375
250 74 767 133 36 189 67 609 120 556
285 4 357 543 82 494 235 606 70 11
278 206 470 430 354 546 183 493 236 440
136 188 653 131 769 15

John E. Franklin · 2005-12-28 15:01:39

Couldn't resist another. My computer is having fun making'm.
1 195 30 699 142 147 753 31 330 399
277 252 189 100 44 181 603 73 503 226
63 133 92 29 7 354 87 82 242 599
185 344 332 452 32 809 91 78 43 57
304 321 520 209 367 33 16 713 128 401
83 358 171 153 472 12 564 112 249 651
25 551 290 610 119 722 62 227 673 111
789 52 48 177 264 136 440 236 248 152
17 512 113 56 88 108 36 364 312 417
67 662 238 438 291 109 60 616 284 500
176 665 64 132 157 327 457 168 28 333
196 429 355 45 684 216 568 161 35 254
475 201 24

John E. Franklin · 2005-12-28 15:04:58

I like this one because it ends with 19 squared, which I always liked.
1 35 86 398 131 310 315 85 84 141
28 501 124 72 769 15 309 267 358 126
18 711 130 159 325 75 214 411 30 6
318 43 182 107 14 386 143 757 27 9
187 489 136 593 307 422 478 251 425 359
170 230 346 54 387 513 163 161 323 518
11 278 347 494 82 647 194 590 139 185
440 44 20 605 179 305 479 97 344 17
272 52 117 612 172 728 113 616 284 40
360

John E. Franklin · 2005-12-28 15:16:06

1 24 12 4 32 49 15 21 60 84
16 33 111 10 39 82 18 7 42 58
6 94 27 54 67 77 44 37 63 81
19 102 123 73 71 154 135 121 168 88
236 53 172 152 137 119 106 150 46 210
79 177 112 144 180 109 147 22 267 57
232 92 197 127 129 40 9 280 120 76
213 187 254 146 295 105 219 222 178 78
118 206 194 31 50 391 93 196 333 108
292 192 169 272 304 225 175 114 327 202
198 126 403 173 83 38 11 473 56 8
136 153 72 217 224 100 476 253 188 212
464 161 128 601 75 501 28 413 163 237
492 184 300 61 3 141 148 176 265 360
216 513 328 297 279 346 330 199 162 322
578 47 2 14 182 74 287 554 230 446
130 231 669 115 326 158 371 529 255 421
363 366 259 582 318 211 518 266 95 530
370 359 41 248 428 472 204 580 261 523
377 23 602 239 245 484 357 543 133 443
86 355 374 467 17 179 605 124 717 183
393 48

John E. Franklin · 2005-12-28 15:23:49

1 8 17 19 6 3 13 12 37 44
5 31 33 48 16 20 29 7 42 22
27 54 10 71 50 14 35 46 75 25
39 61 60 40 9 72 28 53 11 38
43 21 15 66 55 26 23 2 119 77
148 108 36 160 65 191 34 87 169 120
105 91 165 124 132 157 99 45 76 213
111 250 74 95 161 200 89 235 126 18
103 153 171 85 59 110 146 143 113 211
78 147 49 176 80 41 248 152 73 183
217 224 32 368 116 109 375 154 135 394
47 178 222 307 177 264 97 344 185 256
144 340 189 295 234 166 123 201 240 289
195 205 84 277 252 4 525 100 69 460
24 57 267 358 83 206 278 163 413 212
149 335 194 431 145 384 241 288 337 63
226 98 158 326 299 230 170 455 121 408
168 273 88 56 385 291 438 187 542 134
155 101 524 52 477 199 242 82 543 133
92 164 320 305 424 417 67 294 106 623
218 407 269 215 626 274 351 378 298 486
243 333 196 588 312 472 428 356 485 244
285 556 228 613 287 554 122 662 238 86
539 302 139 645 255 421 363 313 416 484
357 268 461 323

John E. Franklin · 2005-12-28 15:30:04

This one is neat because like krassi's, only one number is above 100.
1 15 10 6 19 17 8 28 21 4
5 20 16 9 7 29 35 14 50 31
18 46 3 22 59 41 40 60 61 39
82 62 2 79 65 56 88 33 67 77
23 13 51 70 74 26 55 66 78 43
57 87 34 30 91 53 47 97 24 12
132 37 63
But I guess you could go back to the 24 and stop there, so all are below 100.
krassi_holmz still has a better density staying in the low #'s.

John E. Franklin · 2005-12-28 15:58:07

More to ponder.
1 3 13 12 4 5 11 14 2 7
9 16 20 29 35 46 18 31 33 48
52 69 75 6 10 15 21 28 8 17
19 30 34 47 53 68 32 49 51 70
74 26 23 41 40 24
forty-six long.

John E. Franklin · 2005-12-28 16:05:03

I finally got a nice one!! seventy-two long, all under 100.
1 8 17 19 6 3 13 12 4 5
11 14 2 7 9 16 20 29 35 46
18 31 33 48 52 69 75 25 24 40
41 23 26 10 15 21 28 36 45 55
66 34 30 51 49 32 68 53 47 74
70 99 22 27 37 44 56 65 79 42
39 61 60 84 85 59 62 38 43 57
64 80 Sweet:)

seerj · 2005-12-28 22:42:22

krassi_holmz wrote:

1,3,6,10,15,11,5,4,12,13,23,2,7,9,16,20,29,27,22,14,35
length=21

Seems to be good coz the number are all less than 50, but
Let ps=perfect square
1+3 ps
3+6 ps
6+10 ps
10+15 ps
15+11= 26 isn't a perfect square!
11+5 ps
5+4 ps
4+12 ps
12+13 ps
13+23 ps
23+2 ps
2+7 ps

Almost good. But 15+11 isn't right btw

krassi_holmz · 2005-12-28 22:43:40

You beat me!
:0

seerj · 2005-12-28 22:46:17

Tnx to Franklin too. But I think that all numbers have to be less than 50.
I try to ask but i think that the tips was n<50
So all the circular sequences with n<50 like krassi is doing . [only that 11+15 isn't a perfect square..so the sequence isn't correct ;| ]

krassi_holmz · 2005-12-28 22:47:28

So the other solutions are not solutions.
That's because I calculated them by hand.
Now I'll do some progarmming...

seerj · 2005-12-28 22:51:47

krassi_holmz wrote:

So the other solutions are not solutions.
That's because I calculated them by hand.
Now I'll do some progarmming...

You're great! Thank u in advance. So Did u understand the problem now? It wasn't so difficult but is so difficult to understand which is the minimum n ^^

Thank u all for the work!

krassi_holmz · 2005-12-28 23:58:52

Ha,ha
I've made a program for my algoritm!

krassi_holmz · 2005-12-29 00:06:50

Here's a result:
{1, 3, 6, 10, 15, 21, 4, 5, 11, 14, 2, 7, 9, 16, 20, 29, 35, 46, 18, 31, 33, 48, 52, 12, 13, 23, 26, 38, 43, 57, 24, 25, 39, 42, 22, 27, 37, 44, 56, 8}
Length-40
MaxNumber-57!

Math Is Fun Forum

#51 2005-12-28 00:37:14

Re: Very interesting problems..

#52 2005-12-28 07:10:11

Re: Very interesting problems..

#53 2005-12-28 11:01:46

Re: Very interesting problems..

#54 2005-12-28 11:56:09

Re: Very interesting problems..

#55 2005-12-28 12:02:29

Re: Very interesting problems..

#56 2005-12-28 13:25:09

Re: Very interesting problems..

#57 2005-12-28 13:29:05

Re: Very interesting problems..

#58 2005-12-28 13:35:15

Re: Very interesting problems..

#59 2005-12-28 13:38:25

Re: Very interesting problems..

#60 2005-12-28 13:42:34

Re: Very interesting problems..

#61 2005-12-28 14:44:06

Re: Very interesting problems..

#62 2005-12-28 15:01:39

Re: Very interesting problems..

#63 2005-12-28 15:04:58

Re: Very interesting problems..

#64 2005-12-28 15:16:06

Re: Very interesting problems..

#65 2005-12-28 15:23:49

Re: Very interesting problems..

#66 2005-12-28 15:30:04

Re: Very interesting problems..

#67 2005-12-28 15:58:07

Re: Very interesting problems..

#68 2005-12-28 16:05:03

Re: Very interesting problems..

#69 2005-12-28 22:42:22

Re: Very interesting problems..

#70 2005-12-28 22:43:40

Re: Very interesting problems..

#71 2005-12-28 22:46:17

Re: Very interesting problems..

#72 2005-12-28 22:47:28

Re: Very interesting problems..

#73 2005-12-28 22:51:47

Re: Very interesting problems..

#74 2005-12-28 23:58:52

Re: Very interesting problems..

#75 2005-12-29 00:06:50

Re: Very interesting problems..

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