[seqfan] Re: A new and stubborn "Yellowstone" sequence

[Neil Sloane]

Hugo,  Sorry about that!  Gmail doesn't show signatures,
all you see at the bottom of the email is three dots, ...,
and you have to guess who it is from

Of course one can click the three dots, but who does that?

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com



On Wed, Mar 22, 2017 at 1:35 PM,  <hv at crypt.org> wrote:
> 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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