[math-fun] does anyone recognize ... ?
Does anyone recognize the sum (for n>=1) of log(n+1) -------- n! The numerical value is roughly 1.5586704364253894. My attempts to use ISC found no matches, but I'm no expert on looking for non-obvious matches. Rich
Hi, Rich, Is this related to entropy? Bill -----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of rcs@xmission.com Sent: Monday, August 22, 2011 2:46 PM To: math-fun@mailman.xmission.com Cc: rcs@xmission.com Subject: [math-fun] does anyone recognize ... ? Does anyone recognize the sum (for n>=1) of log(n+1) -------- n! The numerical value is roughly 1.5586704364253894. My attempts to use ISC found no matches, but I'm no expert on looking for non-obvious matches. Rich _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
On 8/29/11, Cordwell, William R <wrcordw@sandia.gov> wrote:
Hi, Rich,
Is this related to entropy?
Bill
-----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of rcs@xmission.com Sent: Monday, August 22, 2011 2:46 PM To: math-fun@mailman.xmission.com Cc: rcs@xmission.com Subject: [math-fun] does anyone recognize ... ?
Does anyone recognize the sum (for n>=1) of
log(n+1) -------- n!
The numerical value is roughly 1.5586704364253894. My attempts to use ISC found no matches, but I'm no expert on looking for non-obvious matches.
Rich
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Hello, me too, I tested the number : 1.5586704364253890428102239834708593333956927955614839145443974035222006762271 836687890293324686544157081366005148135551215282556... on my souped-up version at home ; niet, nothing. I also tried various factorial bases and nothing came out, in last resort, tried identify(); the builtin maple program as well, : nothing. and a home made PSLQ with 126 experiments with various numbers: nothing came out. conclusion : I don't know what is this number. Simon Plouffe Le 29/août/2011 15:43, Fred lunnon a écrit :
On 8/29/11, Cordwell, William R<wrcordw@sandia.gov> wrote:
Hi, Rich,
Is this related to entropy?
Bill
-----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of rcs@xmission.com Sent: Monday, August 22, 2011 2:46 PM To: math-fun@mailman.xmission.com Cc: rcs@xmission.com Subject: [math-fun] does anyone recognize ... ?
Does anyone recognize the sum (for n>=1) of
log(n+1) -------- n!
The numerical value is roughly 1.5586704364253894. My attempts to use ISC found no matches, but I'm no expert on looking for non-obvious matches.
Rich
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The number is the average information loss for a random map from [1,N]->[1,N], measured base e instead of base 2. Divide by ln2 = .693 to get Bits. (For large N, of course.) FWIW, it's in the Shamos list, which gives an extra, weirder, series. I've seen a list similar to Shamos's, with lots more numbers. I'm under the impression that S. Plouffe is the proprietor, but I don't recall the web page. The Plouffe list included more simple numbers, including rationals & roots of quadratics, cubics etc, along with solutions to cos x = x. I had the experience of trying to look up a number I'd calculated empirically - perhaps an estimate of the polyomino ratio - and finding the list had many, many numbers that matched my target: I needed more digits! We need something like Sloane's Superseeker. I'll omit my wish list, since I'm not prepared to write the code. --- While we're on the subject of math-related databases, I'll mention another collection we need: Worked Problems & Puzzles. Mathists generate and solve a lot of problems. Most of these are not profound enough to publish. It would still be worthwhile to collect them, to smooth the path for followers. Collecting is the easy part; the hard task is organization & making it searchable. For example, some of the geometry problems we've discussed over the years: How to make them searchable beyond adding keywords? Searching for "ellipse intersection" is too unspecific. Rich ----- Quoting Simon Plouffe <simon.plouffe@gmail.com>:
Hello,
me too, I tested the number : 1.5586704364253890428102239834708593333956927955614839145443974035222006762271 836687890293324686544157081366005148135551215282556...
on my souped-up version at home ; niet, nothing.
I also tried various factorial bases and nothing came out, in last resort, tried identify(); the builtin maple program as well, : nothing. and a home made PSLQ with 126 experiments with various numbers: nothing came out.
conclusion : I don't know what is this number.
Simon Plouffe
Le 29/août/2011 15:43, Fred lunnon a écrit :
On 8/29/11, Cordwell, William R<wrcordw@sandia.gov> wrote:
Hi, Rich,
Is this related to entropy?
Bill
-----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of rcs@xmission.com Sent: Monday, August 22, 2011 2:46 PM To: math-fun@mailman.xmission.com Cc: rcs@xmission.com Subject: [math-fun] does anyone recognize ... ?
Does anyone recognize the sum (for n>=1) of
log(n+1) -------- n!
The numerical value is roughly 1.5586704364253894. My attempts to use ISC found no matches, but I'm no expert on looking for non-obvious matches.
Rich
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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On Fri, Sep 9, 2011 at 3:31 PM, <rcs@xmission.com> wrote:
While we're on the subject of math-related databases, I'll mention another collection we need: Worked Problems & Puzzles. Mathists generate and solve a lot of problems. Most of these are not profound enough to publish. It would still be worthwhile to collect them, to smooth the path for followers. Collecting is the easy part; the hard task is organization & making it searchable. For example, some of the geometry problems we've discussed over the years: How to make them searchable beyond adding keywords? Searching for "ellipse intersection" is too unspecific.
I'm very interested in helping create or maintain something like this, although my particular interest is in problems suitable for the K12 audience, which has only some overlap with the problems that Rich is thinking of here. So far I don't have any better ideas than tagging things with keywords, some from a pre-cooked list of standard topics and others subject to creation on the spot by the problem contributor. So if anyone knows anything about how to organize a useful database along these lines, please let me know! You can look at http://www.mathcircles.org/content/problem-list for a beginning effort in this direction. --Joshua Zucker
One very useful feature is that any concept or word has links to related concepts & words - synonyms, antonyms, misspellings included. You might define a language that lets you talk about relationships between objects, and try to pattern match (for searching). The ability to modify a search, and suggested modifications, could help. Google does a little of this, but is hardly a model of usability for newcomers. Possible test cases for a matcher: Lookups on subexpressions within expressions, equations, inequalities. Finding subdiagrams within geometry proofs. I suggest abandoning the distinction between student/teacher for purposes of access. The costs are high. Rich ----- Quoting Joshua Zucker <joshua.zucker@gmail.com>:
On Fri, Sep 9, 2011 at 3:31 PM, <rcs@xmission.com> wrote:
While we're on the subject of math-related databases, I'll mention another collection we need: Worked Problems & Puzzles. Mathists generate and solve a lot of problems. Most of these are not profound enough to publish. It would still be worthwhile to collect them, to smooth the path for followers. Collecting is the easy part; the hard task is organization & making it searchable. For example, some of the geometry problems we've discussed over the years: How to make them searchable beyond adding keywords? Searching for "ellipse intersection" is too unspecific.
I'm very interested in helping create or maintain something like this, although my particular interest is in problems suitable for the K12 audience, which has only some overlap with the problems that Rich is thinking of here.
So far I don't have any better ideas than tagging things with keywords, some from a pre-cooked list of standard topics and others subject to creation on the spot by the problem contributor. So if anyone knows anything about how to organize a useful database along these lines, please let me know!
You can look at http://www.mathcircles.org/content/problem-list for a beginning effort in this direction.
--Joshua Zucker
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participants (5)
-
Cordwell, William R -
Fred lunnon -
Joshua Zucker -
rcs＠xmission.com -
Simon Plouffe