Is this a million dollar question? Thane Plambeck 650 321 4884 office 650 323 4928 fax http://www.qxmail.com/home.htm ----- Original Message ----- From: "Richard Guy" <rkg@cpsc.ucalgary.ca> To: "Math Fun" <math-fun@mailman.xmission.com> Sent: Wednesday, November 27, 2002 11:47 AM Subject: [math-fun] (no subject)
Calculate the natural log of (95536/e)^{95536}.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
At 12:47 PM 11/27/02 -0700, you wrote:
Calculate the natural log of (95536/e)^{95536}.
I'm assuming Richard wouldn't have asked this question if there weren't something profound going on ... and the _real_ puzzle is to figure out what it is. The function f(x) = x (ln x - 1) is the integral of ln x. Its values at integer arguments are spaced by ln x, therefore. And so for one of these values to be an integer plus or minus a small p is a surprise on the order of p/2(ln x); we would expect it to happen every 2(ln x)/p integers in the vicinity of x. Near 10^6, we would expect f(x) to be within .001 of an integer about once every 6000 integers. So, this one-in-6000 chance happens for 10^6. I'm impressed enough that I'm sure there's a deeper principle going on. -A
participants (3)
-
Allan C. Wechsler -
Richard Guy -
Thane Plambeck