谢谢各位。13是对的。链接https://oeis.org/A084829/a084829.txt
yma16
2022-02-15 07:35:57
( reads)
# Densest Packings of n Equal Spheres in a Sphere of Radius 1. # Largest Possible Radii # The results by Th. Gensane are published in the article # Dense Packings of Equal Spheres in a Larger Sphere, # Les Cahiers du LMPA J. Liouville 188, 2003 # Th. Gensane's data for n>40 are from private communication Nov 2005. # Dave Boll only gave the radii without providing sphere locations. # A comprehensive update is now performed based on the results # provided in a private communication by Liang Yu; see WenQi Huang, Liang Yu: # Serial Symmetrical Relocation Algorithm for the Equal Sphere Packing Problem # http://arxiv.org/abs/1202.4149 # All results provided by Liang Yu, which were accurate only to ~= 10^-8, # have been improved in precision by application of a multi-scale # shaking process. The expected precision is now better than 10^-12. # Author: Hugo Pfoertner http://www.pfoertner.org/ # URL of this file: http://www.randomwalk.de/sphere/insphr/spisbest.txt # Date of last update: YYYY MM DD 2013 08 25 #n Radius Originator 1 1.000000000000000 'common sense' 2 0.500000000000000 'common sense' 3 0.464101615137755 'Tammes sol.' 4 0.449489742783178 'Tammes sol.' 5 0.414213562373095 'Tammes sol.' 6 0.414213562373095 'Tammes sol.' 7 0.385913557399473 'Tammes sol.' 8 0.378024844800586 'Tammes sol.' 9 0.366025403784434 'Tammes sol.' 10 0.353049430235565 'Tammes sol.' 11 0.344576516755255 'Tammes sol.' 12 0.344576516755255 'Tammes sol.' 13 0.333333333333333 'Tammes sol.+0' 14 0.323504674182003 'Tammes sol.+0' 15 0.318304823107090 'Tammes sol.+0' 16 0.310975923320006 'Tammes sol.+0' 17 0.305693961648916 'Tammes sol.+0' 18 0.301296588595412 'Tammes sol.+0' 19 0.295332333638629 'Tammes sol.+0' 20 0.287890825548632 'Tammes sol.+0' 21 0.286832818044709 'Tammes sol.+0' 22 0.279342623828187 'Tammes sol.+0' 23 0.275670699448662 'Tammes sol.+0' 24 0.271341306094153 'Thierry Gensane' 25 0.271191827927395 'Tammes sol.+0' 26 0.266851270146397 'Thierry Gensane' 27 0.262232079867910 'Thierry Gensane' 28 0.260305474106206 'Thierry Gensane' 29 0.257925461381016 'Thierry Gensane' 30 0.255330557201847 'Thierry Gensane' 31 0.253116205096448 'Dave Boll' 32 0.250787447430689 'Thierry Gensane' 33 0.2487624 'Thierry Gensane' / best LY,HP: 0.248762333488756 34 0.247052660950443 'Thierry Gensane' 35 0.244833654976580 'Thierry Gensane' 36 0.243132162305941 'Thierry Gensane' 37 0.240686554958030 'Thierry Gensane' 38 0.240519371740801 'Liang Yu' / TG 2003: 0.24051470 39 0.236745238676494 'Thierry Gensane' 40 0.234999232359232 'Thierry Gensane' 41 0.232755979195002 'Thierry Gensane' 42 0.2321190 'Dave Boll' / questionable; best LY,HP: 0.232118614012800 43 0.229732953802005 'Thierry Gensane' 44 0.228163031287400 'Liang Yu' / TG 2005: 0.22815860 45 0.226911553062939 'Thierry Gensane' 46 0.225168195856191 'Dave Boll' 47 0.223507034454931 'Thierry Gensane' 48 0.222405937993816 'Thierry Gensane' 49 0.221278176587584 'Liang Yu' 50 0.219758275473346 'Liang Yu' 51 0.218550275685041 'Liang Yu' / HP 2006: 0.2178888 52 0.216930402454011 'Liang Yu' / HP 2006: 0.2167665 53 0.216288054714919 'Liang Yu' / HP 2006: 0.2157772 54 0.214920660994050 'Liang Yu' / HP 2006: 0.2146846 55 0.213441684044414 'Liang Yu' / HP 2006: 0.2132680 56 0.213067867576129 'Liang Yu' / HP 2006: 0.2126136 57 0.211309355482316 'Liang Yu' / HP 2006: 0.2108661 58 0.210480099018006 'Liang Yu' / HP 2006: 0.2103022 59 0.209759446545646 'Liang Yu' / HP 2006: 0.2096252 60 0.209426992286691 'Hugo Pfoertner' 61 0.209108658611283 'Liang Yu' / HP 2006: 0.2089123 62 0.206739152059719 'Liang Yu' / HP 2006: 0.2058170 63 0.205954915018959 'Liang Yu' / HP 2006: 0.2047140 64 0.204087153397427 'Liang Yu' / HP 2006: 0.2036646 65 0.203076034012903 'Liang Yu' / HP 2006: 0.2027475 66 0.202108753938119 'Liang Yu' / HP 2006: 0.2019158 67 0.201216625855546 'Liang Yu' / HP 2006: 0.2004429 68 0.200002226173858 'Liang Yu' / HP 2006: 0.1997220 69 0.199281531977205 'Liang Yu' / HP 2006: 0.1987922 70 0.198688727945893 'Liang Yu' / HP 2006: 0.1983310 71 0.197222124167297 'Liang Yu' / HP 2006: 0.1969787 72 0.196285910453337 'Liang Yu' / HP 2006: 0.1958001