And if he lives another decade to 2022, his age will equal the size of his discovery in 1978 (110B; 22 squares with a side of 110 - also the smallest possible side in a perfect squared square!) On Thu, Apr 19, 2012 at 2:59 AM, <math-fun-request@mailman.xmission.com>wrote:
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Today's Topics:
1. superstring theory solves math problems? (Warren Smith) 2. n and n^3 have all digits odd (James Buddenhagen) 3. Re: n and n^3 have all digits odd (Charles Greathouse) 4. Re: n and n^3 have all digits odd (Hans Havermann) 5. THW (Theophilus Harding Willcocks), is 100 today, Happy Birthday! (Stuart Anderson) 6. Re: n and n^3 have all digits odd (Charles Greathouse) 7. Re: THW (Theophilus Harding Willcocks), is 100 today, Happy Birthday! (Henry Baker)
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Message: 1 Date: Tue, 17 Apr 2012 15:38:06 -0400 From: Warren Smith <warren.wds@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Subject: [math-fun] superstring theory solves math problems? Message-ID: <CAAJP7Y0WF7bZOw=nez3k85mJhZ03+RRjs3R_uqZqcP9kJt4NRg@mail.gmail.com
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http://www.ams.org/journals/bull/2000-37-04/S0273-0979-00-00875-2/S0273-0979...
describes a remarkable conjectured formula (arising from generating functions ad series reversions) for the number of rational curves of degree d on a generic "quintic threefold." The formula gives the right answers for the first 9 cases. However, it is not even clear that the numbers it outputs, are always integers, although hundreds have been computed and always came out integer.
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Message: 2 Date: Wed, 18 Apr 2012 10:09:19 -0500 From: James Buddenhagen <jbuddenh@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Subject: [math-fun] n and n^3 have all digits odd Message-ID: <CAL_+dT+MFANb8eH06pnDa4qK7uSVOXOTM7d9oiHBiS51y81v8g@mail.gmail.com
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Suppose the positive integers n and n^3 both have all digits odd. Such numbers include 1, 11, 15, 33, 39, 71, 91, 173, 175, 179, 335, 3337, 5597, 7353. Is this list complete? This sequence is http://oeis.org/A085597 in OEIS. But there is no key word indicating that it is a finite sequence. Is this known to be a finite sequence?
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Message: 3 Date: Wed, 18 Apr 2012 11:48:46 -0400 From: Charles Greathouse <charles.greathouse@case.edu> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] n and n^3 have all digits odd Message-ID: <CAAkfSGLkakN5ryKJ5AJbW5hxacryMc5+V8Gq3QmnA+nKjgVhmQ@mail.gmail.com
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I don't think it has been proven to be finite, though it surely is -- there are 5^n n-digit numbers with all digits odd, but the 'chance' that a 3n-digit number has all digits odd is 2^(-3n). (That the last few digits are OK doesn't matter, asymptotically.) The sum of (5/8)^n is of course finite.
Charles Greathouse Analyst/Programmer Case Western Reserve University
On Wed, Apr 18, 2012 at 11:09 AM, James Buddenhagen <jbuddenh@gmail.com> wrote:
Suppose the positive integers n and n^3 both have all digits odd. Such numbers include 1, 11, 15, 33, 39, 71, 91, 173, 175, 179, 335, 3337, 5597, 7353. ?Is this list complete? ?This sequence is http://oeis.org/A085597 in OEIS. ?But there is no key word indicating that it is a finite sequence. ?Is this known to be a finite sequence?
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Message: 4 Date: Wed, 18 Apr 2012 12:17:28 -0400 From: Hans Havermann <gladhobo@teksavvy.com> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] n and n^3 have all digits odd Message-ID: <27A146BD-7C0D-4129-B481-00B4FA1B9932@teksavvy.com> Content-Type: text/plain; charset=US-ASCII; format=flowed; delsp=yes
James Buddenhagen:
Is this known to be a finite sequence?
I think the best we can ever really do with this sort of problem is conjecture it to be true and provide a large number up to which it is known to be true. There was another such question brought up recently on SeqFan asking if 34155 is the only odd number equal to the sum of its proper divisors greater than (or equal to) its square root.
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Message: 5 Date: Thu, 19 Apr 2012 02:21:12 +1000 From: Stuart Anderson <stuart.errol.anderson@gmail.com> To: math-fun@mailman.xmission.com Cc: George Jelliss <george.jelliss@virgin.net>, Dom Guerin <nietzscheplayedchess@gmail.com>, Sascha Kurz <sascha.kurz@uni-bayreuth.de>, Lorenz Milla <lorenz.milla@gmx.net>, Ed Pegg Jr <ed@mathpuzzle.com>, Steve Johnson <stevejohnson2@verizon.net>, geoffrey morley <ghmorley@gmail.com
, efriedma@stetson.edu, Richard Guy <rkg@cpsc.ucalgary.ca> Subject: [math-fun] THW (Theophilus Harding Willcocks), is 100 today, Happy Birthday! Message-ID: <CA+3-r9NLO45i+tJ3h1=BN5hnLPnoHkjwJ9+QP3miM0jcew1Myg@mail.gmail.com
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Theophilus Harding Willcocks, squarer of squares and chess enthusiast turns 100 today, 19th April 2012!
http://www.squaring.net/history_theory/th_willcocks.html
Stuart Anderson
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Message: 6 Date: Wed, 18 Apr 2012 12:31:22 -0400 From: Charles Greathouse <charles.greathouse@case.edu> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] n and n^3 have all digits odd Message-ID: <CAAkfSGL1C=OghNQfOWQ=sqQHpao82eqGFKkaT+z+xhrqO0kJ1g@mail.gmail.com
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I think there's hope in the case of the 34155 conjecture. There are powerful techniques available using sigma_{-1} which might be brought to bear.
I feel like the 2e11 lower bound could be used to find a narrow range (2, 2.00...] in which sigma_{-1}(n) must reside, and then... well, I don't know or else I'd try to prove it myself. But in any case the odd digit problem looks much less amenable to solution.
Charles Greathouse Analyst/Programmer Case Western Reserve University
On Wed, Apr 18, 2012 at 12:17 PM, Hans Havermann <gladhobo@teksavvy.com> wrote:
James Buddenhagen:
Is this known to be a finite sequence?
I think the best we can ever really do with this sort of problem is conjecture it to be true and provide a large number up to which it is known to be true. There was another such question brought up recently on SeqFan asking if 34155 is the only odd number equal to the sum of its proper divisors greater than (or equal to) its square root.
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Message: 7 Date: Wed, 18 Apr 2012 09:57:45 -0700 From: Henry Baker <hbaker1@pipeline.com> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] THW (Theophilus Harding Willcocks), is 100 today, Happy Birthday! Message-ID: <E1SKYDQ-0004eO-Rs@elasmtp-scoter.atl.sa.earthlink.net> Content-Type: text/plain; charset="us-ascii"
We look forward to his birthday in 2033 !
At 09:21 AM 4/18/2012, you wrote:
Theophilus Harding Willcocks, squarer of squares and chess enthusiast turns 100 today, 19th April 2012!
http://www.squaring.net/history_theory/th_willcocks.html
Stuart Anderson
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End of math-fun Digest, Vol 110, Issue 18 *****************************************