[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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