tag:blogger.com,1999:blog-7225373.post368825393797326147..comments2024-02-29T03:34:23.190-05:00Comments on Who Were the Sea Peoples?: What's the Next Term IIgcallahhttp://www.blogger.com/profile/10065877215969589482noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-7225373.post-91637601286701756252008-02-10T16:21:00.000-05:002008-02-10T16:21:00.000-05:00Larry -I used Stirling's formula in the form: log ...Larry -<BR/><BR/>I used Stirling's formula in the form: log n! approximately =<BR/>(n+0.5) log n - 0.4343n + 0.3991.<BR/>Those coefficients checked out when I recalculated them, but, obviously, my arithmetic didn't, cuz when I redid it for 720!, I got roughly 2x10^1746. Sorry.Wabulonhttps://www.blogger.com/profile/16838347174718251102noreply@blogger.comtag:blogger.com,1999:blog-7225373.post-41490345485709564212008-02-06T15:59:00.000-05:002008-02-06T15:59:00.000-05:00Yes, but Wabulon, how are we supposed to guess the...Yes, but Wabulon, how are we supposed to guess the formula if one of the items in the series is wrong?gcallahhttps://www.blogger.com/profile/10065877215969589482noreply@blogger.comtag:blogger.com,1999:blog-7225373.post-21277783729032273542008-02-06T14:12:00.000-05:002008-02-06T14:12:00.000-05:00Err, uhh, I used Stirling's Formula (quite accurat...Err, uhh, I used Stirling's Formula (quite accurate for approximating large factorials), log10-ing everything. And, no, I am not particularly good at arithmetic (although I have a nice essay on Peano's Postulates if anyone wants to see it). And, of course, I really don't much care what the actual value of 720! is, it's the principle of the thing...Wabulonhttps://www.blogger.com/profile/16838347174718251102noreply@blogger.comtag:blogger.com,1999:blog-7225373.post-61656414098917550212008-02-06T13:26:00.000-05:002008-02-06T13:26:00.000-05:00Yes, funcs.bc provides it (and at least on Linux t...Yes, funcs.bc provides it (and at least on Linux that's what implements factorial(), so I assume you have it). For example:<BR/><BR/>engnot(factorial(720), 5)<BR/>2.60121*10^1746LarryRuanehttps://www.blogger.com/profile/13187331388492812355noreply@blogger.comtag:blogger.com,1999:blog-7225373.post-23750080990099560442008-02-06T12:42:00.000-05:002008-02-06T12:42:00.000-05:00Larry, is there a way to force bc to output in sci...Larry, is there a way to force bc to output in scientific notation?gcallahhttps://www.blogger.com/profile/10065877215969589482noreply@blogger.comtag:blogger.com,1999:blog-7225373.post-1056565731788303292008-02-06T12:38:00.000-05:002008-02-06T12:38:00.000-05:00I get the same answer on Max OS X bc -- which, of ...I get the same answer on Max OS X bc -- which, of course, is the same program, so no surprise. The question I have is, "Do we have reason to think bc is reliable for such huge numbers?"<BR/><BR/>(Of course, another question is, "Do we have reason to think Wabulon is reliable for such huge numbers?")gcallahhttps://www.blogger.com/profile/10065877215969589482noreply@blogger.comtag:blogger.com,1999:blog-7225373.post-6080217476269270942008-02-06T12:21:00.000-05:002008-02-06T12:21:00.000-05:00Are you sure about 3!!!? Using linux bc -l funcs....Are you sure about 3!!!? Using linux bc -l funcs.bc, both "factorial(720)" and "factorial(factorial(factorial(3)))" produce:<BR/><BR/>26012189435657951002049032270810436111915218750169457857275418378508\<BR/>35631156947382240678577958130457082619920575892247259536641565162052\<BR/>01587379198458774083252910524469038881188412376434119195104550534665\<BR/>86162432719401971139098455367272785370993456298555867193697740700037\<BR/>00430783758997420676784016967207846280629229032107161669867260548988\<BR/>44551425719398549944893959449606404513236214026598619307324936977047\<BR/>76060676806701764916694030348199618814556251955925669188308255149429\<BR/>47596537274845624628824234526597789737740896466553992435928786212515\<BR/>96748322097602950569669992728467056374713753301924831358707612541268\<BR/>34158601294475660114554207495899525635430682886346310849656506827715\<BR/>52996256790845235702552186222358130016700834523443236821935793184701\<BR/>95651072978180435417389056072742804858399591972902172661229129842051\<BR/>60675790362323376994539641914751755675576953922338030568253085999774\<BR/>41675784352815913461340394604901269542028838347101363733824484506660\<BR/>09334848444071193129253769465735433737572477223018153403264717753198\<BR/>45373414786743270484579837866187032574059389242157096959946305575210\<BR/>63203263493209220738320923356309923267504401701760572026010829288042\<BR/>33560664308988871029738079757801305604957634283868305719066220529117\<BR/>48225105366977566030295740433879834715185526028053338663571391010463\<BR/>36419769097397432285994219837046979109956303389604675889865795711176\<BR/>56667003915674815311594398004362539939973120306649060132531130471902\<BR/>88984918562037666691644687911252491937544258458950003115616829743046\<BR/>41142538074897281723375955380661719801404677935614793635266265683339\<BR/>50976000000000000000000000000000000000000000000000000000000000000000\<BR/>00000000000000000000000000000000000000000000000000000000000000000000\<BR/>00000000000000000000000000000000000000000000000<BR/><BR/>which has around 1746 digits, not 2466. Great puzzle though; thanks for posting it.LarryRuanehttps://www.blogger.com/profile/13187331388492812355noreply@blogger.comtag:blogger.com,1999:blog-7225373.post-1609547690581255532008-02-06T07:51:00.000-05:002008-02-06T07:51:00.000-05:00"4!!!! is a rather large number in most contexts."..."4!!!! is a rather large number in most contexts."<BR/><BR/>But not that of, "Shots of well vodka consumed by Wabulon at B61.gcallahhttps://www.blogger.com/profile/10065877215969589482noreply@blogger.com