User:Vaughan Pratt

Blog (of sorts)


Which subject, please! In; Later life and research Ayrton delivered papers on the subject again before the Royal Society in 1908 and 1911; she also presented the results of her research

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In 2010, 40 years after getting my Ph.D. in computer science, I switched to geophysics, for which my undergraduate degrees in mathematics and physics were very helpful. 

Shellsort
Your twos-and-threes Shellsort is very clever. Please, are questions allowed?

• In macro structure, it has gaps that grow faster than arithmetically, yet slower than geometrically. I like.

• Would it be faster still if nudged for coprimality? The proof would fail, but would shellsort be faster? So the gaps could be {1,2} then the values of 2^Sqrt[ n Log[9]/Log[2] ], n≥1, except that each is replaced with the nearest integer coprime to all smaller except 1.

[deleted]


 * Slight change. rather than fit to sequence, use gaps in sequences. So gaps start 1; subsequent are the nearest integer to Exp[Sqrt[2 Log[3] Log[2] + Log[prevGap]^2]] that is coprime to all smaller except 1.


 * Hence 1 3 5 8 11 13 17 23 29 37 47 59 71 83 97 113 133 157 181 211 241 277 317 359 409 463 523 587 661 743 829 929 1039 1163 1297 1439 1597 1763 1951 2153 2377 2621 2887 3169 3491 3833 4201 4603 5039 5507 6011 6553 7151 7789 8479 9221 10009 10867 11789 12781 13843 14983 16217 17539 18959 20477 22109 23857 25717 27707 29839 32119 34549 37157 39937 42901 46061 49433 53017 56843 60923 65269 69899 74821 80051 85619 91537 97829 104513 111611 119143 127139 135623 144629 154171 164291 175013 186377 198413 211153 224657 238943 254053 270037 286961 304841 323753 343727 364831 387137 410687 435553 461801 489493 518717 549551 582073 616367 652523 690629 730783 773093 817669 864613 914041 966079 1020853 1078489 1139137 1202939 1270051 1340627 1414837 1492837 1574821 1660979 1751507 1846609 1946501 2051389 2161531 2277157 2398537 2525923 2659571 2799809 2946917 3101207 3263009 3432659 3610531 3796963 3992357 4197131 4411679 4636441 4871869 5118439 5376647 5646997 5930017 6226279 6536351 6860837 7200359 7555571 7927147 8315803 8722271 9147293 9591677 10056247 10541851 11049397 11579803 12134033 12713087 13318013 13949879 14609839 15299041 16018703 16770079 17554507 18373321 19227941 20119843 21050563 22021661 23034793 24091667 25194061 26343817 27542831 28793099 30096679 31455701 32872387 34349041 35888029 37491833 39163039 40904299 42718391 44608169 46576597 48626759 50761853 52985197 55300229 57710489 60219697 62831641 65550319 68379833 71324441 74388551 77576747 80893759 84344501 87934051 91667683 95550839 99589187 103788577 108155057 112694929 117414683 122321047 127420987 132721717 138230711 143955697 149904679 156085927 162508019 169179841 176110549 183309653 190786987 198552703 206617339 214991779 223687273 232715479 242088437 251818607 261918863 272402551 283283443 294575797 306294337 318454303 331071437 344162023 357742907 371831477 386445713 401604211 417326177 433631477 450540619 468074809 486255971 505106731 524650471 544911359 565914359 587685271 610250723 633638249 657876253 682994107 709022113 735991589 763934867 792885323 822877439 853946809 886130191 919465523 953991971 989749973 1026781267 1065128941 1104837467 1145952739 1188522131 1232594533 1278220393 1325451791 1374342439 1424947729 1477324921 1531532987 1587632807 1645687201 1705760941 1767920857 1832235887 1898777159 1967617999 2038834043 2112503321

Would this be foolish?

Contact info at http://www.jdawiseman.com/author.html

JDAWiseman (talk) 21:02, 1 October 2019 (UTC)

Sorry, only saw this just now.

You have 28 numbers up to 661, but ceil(log₂(661)*log₃(661)/2) = 28. So I don't see any gain. Vaughan Pratt (talk) 20:03, 24 July 2023 (UTC)