[seqfan] Re: A new and stubborn "Yellowstone" sequence
hv at crypt.org
hv at crypt.org
Wed Mar 22 18:35:01 CET 2017
Neil Sloane <njasloane at gmail.com> wrote:
:Here is the flaw in that argument. When we
:see a type I prime, say a(n) = p, after a(n-1) = x,
:then gcd(x,p)=1. If there were a smaller missing number than p,
:we would use it instead of p provided it was relatively prime to x.
:But that's the rub.
Ah yes, I had known that at some point, apologies for mislaying it.
For what it's worth, here is the sequence of lengths if you split the
sequence at each point satisfied:
1 2 3 4 3 10 4 3 4 4 10 6 8 3 4 17 4 4 9 17 7 4 4 4 5 4 13 4 20 12 14 44 3 4
13 11 4 10 11 8 11 4 16 4 4 9 8 4 20 15 6 7 16 4 6 4 8 21 14 4 26 4 15 6 4 6
12 28 23 20 10 10 52 12 10 19 4 21 4 16 11 16 7 5 8 32 4 4 4 4 8 15 8 4 30 40
3 19 24 4 8 4 12 24 17 16 12 8 13 4 31 25 4 28 14 17 4 4 18 6 4 11 4 9 10 8 4
9 4 4 6 12 24 11 10 19 8 12 8 36 36 16 4 6 7 4 4 36 9 23 41 12 36 26 22 6 44
47 4 8 16 28 8 4 3 27 4 33 19 14 4 28 18 14 5 21 8 23 48 9 11 36 15 43 54 8 4
4 4 42 10 8 4 11 4 4 22 14 13 6 48 4 4 6 31 14 27 78 15 25 4 20 44 8 4 4 28 6
47 14 4 8 15 6 57 15 8 23 35 32 53 36 4 12 20 12 23 10 14 23 8 17 15 4 57 26
10 100 4 4 17 11 52 4 19 5 4 19 32 7 8 8 32 14 21 5 18 48 31 14 4 8 4 54 30 4
5 17 22 27 58 20 17 4 14 10 14 6 11 12 19 12 17 15 55 50 5 9 16 34 6 34 4 4
14 8 32 14 56 24 20 7 58 58 20 4 20 41 12 27 26 40 11 22 15 17 25 19 31 4 12
25 7 22 4 29 12 45 14 23 31 8 29 34 8 4 27 38 8 8 11 4 34 16 55 6 18 53 23 74
12 11 18 39 7 15 4 8 8 7 8 64 15 16 9 20 8 24 8 4 19 13 4 58 24 8 13 77 11 19
8 12 17 102 20 4 41 14 18 16 4 13 8 4 13 12 20 26 12 4 10 33 47 18 55 18 4 24
12 19 8 8 4 14 28 32 37 4 32 12 47 28 7 4 42 8 19 29 23 16 39 13 7 46 12 4 7
39 45 44 41 4 4 17 12 19 12 8 14 79 4 10 58 24 14 24 10 29 100 8 21 26 25 4 8
30 8 62 35 12 20 7 23 76 20 24 27 19 15 41 28 4 20 12 52 18 27 36 10 20 12 7
43 8 59 4 12 43 25 28 8 42 4 21 98 12 17 4 13 4 113 24 15 22 16 24 84 4 22 10
24 42 5 12 8 12 37 21 22 4 49 11 16 36 69 33 4 29 66 17 10 30 30 4 40 36 22
.. which are trending upwards, but surprisingly slowly.
I see that 4 remains a popular length throughout; here are the first few of
those, which might merit some further study:
5 10 12 9
17 34 30 45
23 46 36 27
25 35 42 48
43 86 66 99
53 106 90 135
59 118 96 81
73 146 130 325
79 158 138 207
83 166 140 175
97 194 150 225
103 206 168 147
137 274 278 139
157 314 306 459
181 362 342 513
193 386 364 637
197 394 368 529
223 446 380 475
251 502 460 575
263 526 468 507
281 562 498 747
293 586 520 845
313 626 570 855
401 802 798 1197
419 838 820 1025
461 922 924 1617
463 926 928 841
467 934 930 1395
479 958 936 1053
503 1006 960 1125
557 1114 1086 1629
569 1138 1100 1375
613 1226 1206 1809
631 1262 1266 1899
659 1318 1322 661
673 1346 1326 1989
691 1382 1362 2043
709 1418 1374 2061
739 1478 1404 1521
751 1502 1420 1775
757 1514 1422 2133
853 1706 1578 2367
863 1726 1602 2403
877 1754 1614 2421
971 1942 1940 2425
:Hans
I'm still not Hans. :)
Hugo
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