[math-fun] Dan Hoey
I just learned of the death of Dan Hoey last fall. http://www.washingtonpost.com/local/obituaries/daniel-j-hoey-computer-specia... -- Thane Plambeck tplambeck@gmail.com http://counterwave.com/
5420976318, 5630187924, 9071532486, etc. In those numbers K, all products of touching digits are visible in K itself (as a substring). For the first K, for instance, the product 5x4 ("20") is a substring of K, as are 4x2 ("8"), 2x0 ("0"), 0x9 ("0"), 9x7 ("63"), 7x6 ("42"), 6x3 ("18"), 3x1 ("3") and 1x8 ("8"). Will you find all such integers -- or at least the smallest and the biggest ones? K integers MUST be 10-digit long and those ten digits must be different one from another. Hope this is not old hat... Best, and HNY to everyone! É.
Eric, Nice sequence! It is now A208981. It needs more terms, in case anyone wants to help. Neil On Mon, Jan 2, 2012 at 6:48 PM, Eric Angelini <Eric.Angelini@kntv.be> wrote:
5420976318, 5630187924, 9071532486, etc. In those numbers K, all products of touching digits are visible in K itself (as a substring). For the first K, for instance, the product 5x4 ("20") is a substring of K, as are 4x2 ("8"), 2x0 ("0"), 0x9 ("0"), 9x7 ("63"), 7x6 ("42"), 6x3 ("18"), 3x1 ("3") and 1x8 ("8"). Will you find all such integers -- or at least the smallest and the biggest ones? K integers MUST be 10-digit long and those ten digits must be different one from another. Hope this is not old hat... Best, and HNY to everyone! É.
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-- Dear Friends, I will soon be retiring from AT&T. New coordinates: Neil J. A. Sloane, President, OEIS Foundation 11 South Adelaide Avenue, Highland Park, NJ 08904, USA Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com
Neil Sloane wrote:
Eric, Nice sequence! It is now A208981. It needs more terms, in case anyone wants to help. Neil
On Mon, Jan 2, 2012 at 6:48 PM, Eric Angelini <Eric.Angelini@kntv.be> wrote:
5420976318, 5630187924, 9071532486, etc.
Ironically, only 19 of the 58 terms appear in the already-submitted A198298 with 5420976318 being the 20th. This is an instance where a Google search will tell you more than an OEIS search.
I generalized this problem to the same problem in base b, instead of base 10. I wrote a backtracking program to calculate the number of such sequences for base b=2 through 13. Here are the numbers 2,6,14,20,27,68,41,29,58,20,0,18. The big surprise is that there were no such sequences in base 12. This sequence isn't in the OEIS. I'll submit it tomorrow. Victor On Sun, Mar 4, 2012 at 2:00 AM, Neil Sloane <njasloane@gmail.com> wrote:
Eric, Nice sequence! It is now A208981. It needs more terms, in case anyone wants to help. Neil
On Mon, Jan 2, 2012 at 6:48 PM, Eric Angelini <Eric.Angelini@kntv.be> wrote:
5420976318, 5630187924, 9071532486, etc. In those numbers K, all products of touching digits are visible in K itself (as a substring). For the first K, for instance, the product 5x4 ("20") is a substring of K, as are 4x2 ("8"), 2x0 ("0"), 0x9 ("0"), 9x7 ("63"), 7x6 ("42"), 6x3 ("18"), 3x1 ("3") and 1x8 ("8"). Will you find all such integers -- or at least the smallest and the biggest ones? K integers MUST be 10-digit long and those ten digits must be different one from another. Hope this is not old hat... Best, and HNY to everyone! É.
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-- Dear Friends, I will soon be retiring from AT&T. New coordinates:
Neil J. A. Sloane, President, OEIS Foundation 11 South Adelaide Avenue, Highland Park, NJ 08904, USA Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
In case you're interested, here are the sequences for base 11 and base 13: 20 sequences of length 11 ["379061A4258","3791A425806","425067391A8","4251A806739","4251A873906","58061A42379","581A4237906", "603791A4258","604251A8739","60581A42379","609371A4258","609573241A8","61A42379058","61A42580379", "61A42580937","673904251A8","67391A80425","937061A4258","9371A425806","9573241A806"] 0 sequences of length 12 18 sequences of length 13 ["315C0926A48B7","31907B26A485C","348B70926A15C","348B715C0926A","5BA862170C439","5BA8621C43907", "5C26A4831B709","705BA8621C439","7B26A485C0319","905C26A4831B7","926A0348B715C","926A15C0348B7", "926A48B70315C","9CB5843170A26","A2609CB584317","B0C6298A43157","C43905BA86217","C6298A431570B"] On Sun, Mar 4, 2012 at 11:15 PM, Victor Miller <victorsmiller@gmail.com> wrote:
I generalized this problem to the same problem in base b, instead of base 10. I wrote a backtracking program to calculate the number of such sequences for base b=2 through 13. Here are the numbers 2,6,14,20,27,68,41,29,58,20,0,18.
The big surprise is that there were no such sequences in base 12. This sequence isn't in the OEIS. I'll submit it tomorrow.
Victor
On Sun, Mar 4, 2012 at 2:00 AM, Neil Sloane <njasloane@gmail.com> wrote:
Eric, Nice sequence! It is now A208981. It needs more terms, in case anyone wants to help. Neil
On Mon, Jan 2, 2012 at 6:48 PM, Eric Angelini <Eric.Angelini@kntv.be> wrote:
5420976318, 5630187924, 9071532486, etc. In those numbers K, all products of touching digits are visible in K itself (as a substring). For the first K, for instance, the product 5x4 ("20") is a substring of K, as are 4x2 ("8"), 2x0 ("0"), 0x9 ("0"), 9x7 ("63"), 7x6 ("42"), 6x3 ("18"), 3x1 ("3") and 1x8 ("8"). Will you find all such integers -- or at least the smallest and the biggest ones? K integers MUST be 10-digit long and those ten digits must be different one from another. Hope this is not old hat... Best, and HNY to everyone! É.
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-- Dear Friends, I will soon be retiring from AT&T. New coordinates:
Neil J. A. Sloane, President, OEIS Foundation 11 South Adelaide Avenue, Highland Park, NJ 08904, USA Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Victor Miller:
I wrote a backtracking program to calculate the number of such sequences for base b=2 through 13. Here are the numbers 2,6,14,20,27,68,41,29,58,20,0,18.
I believe that you may have included in your count numbers that begin with a zero.
On Monday 05 March 2012 05:23:17 Hans Havermann wrote:
Victor Miller:
I wrote a backtracking program to calculate the number of such sequences for base b=2 through 13. Here are the numbers 2,6,14,20,27,68,41,29,58,20,0,18.
I believe that you may have included in your count numbers that begin with a zero.
Quite right, too. Don't you think that's more natural? -- g
Yes, I did. I viewed these sequences as permutations of 0..(b-1) instead of as b-digit numbers. Victor On Mon, Mar 5, 2012 at 4:21 AM, Gareth McCaughan <gareth.mccaughan@pobox.com> wrote:
On Monday 05 March 2012 05:23:17 Hans Havermann wrote:
Victor Miller:
I wrote a backtracking program to calculate the number of such sequences for base b=2 through 13. Here are the numbers 2,6,14,20,27,68,41,29,58,20,0,18.
I believe that you may have included in your count numbers that begin with a zero.
Quite right, too. Don't you think that's more natural?
-- g _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
On Monday 05 March 2012 05:23:17 Hans Havermann wrote:
Victor Miller:
I wrote a backtracking program to calculate the number of such sequences for base b=2 through 13. Here are the numbers 2,6,14,20,27,68,41,29,58,20,0,18.
I believe that you may have included in your count numbers that begin with a zero.
Gareth McCaughan:
Quite right, too. Don't you think that's more natural?
If by 'natural' you mean 'complete', yes. I was trying to ascertain why the counts were different for bases 2-5 & 7-8 from Jean-Paul Davalan's solution sets at the bottom of this page: http://www.cetteadressecomportecinquantesignes.com/DixChiffres.htm
Here are a few more members of the sequences (here's the whole sequence starting at 1): 1,2,6,14,20,27,68,41,29,58,20,0,18,25,0,0 Hmm. Lot's of 0's. Victor On Mon, Mar 5, 2012 at 9:25 AM, Hans Havermann <gladhobo@teksavvy.com> wrote:
On Monday 05 March 2012 05:23:17 Hans Havermann wrote:
Victor Miller:
I wrote a backtracking program to calculate the number of such sequences for base b=2 through 13. Here are the numbers 2,6,14,20,27,68,41,29,58,20,0,18.
I believe that you may have included in your count numbers that begin with a zero.
Gareth McCaughan:
Quite right, too. Don't you think that's more natural?
If by 'natural' you mean 'complete', yes. I was trying to ascertain why the counts were different for bases 2-5 & 7-8 from Jean-Paul Davalan's solution sets at the bottom of this page:
http://www.cetteadressecomportecinquantesignes.com/DixChiffres.htm
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17 has 10 such permutations, and 18 has exactly 1. Computational challenge: find the unique permutation of 0..17 which has the property that the product of two consecutive elements when written in base 17 (and is not 1 digit in base 17) appears somewhere in this permutation. Victor On Mon, Mar 5, 2012 at 5:00 PM, Victor Miller <victorsmiller@gmail.com> wrote:
Here are a few more members of the sequences (here's the whole sequence starting at 1):
1,2,6,14,20,27,68,41,29,58,20,0,18,25,0,0
Hmm. Lot's of 0's.
Victor
On Mon, Mar 5, 2012 at 9:25 AM, Hans Havermann <gladhobo@teksavvy.com> wrote:
On Monday 05 March 2012 05:23:17 Hans Havermann wrote:
Victor Miller:
I wrote a backtracking program to calculate the number of such sequences for base b=2 through 13. Here are the numbers 2,6,14,20,27,68,41,29,58,20,0,18.
I believe that you may have included in your count numbers that begin with a zero.
Gareth McCaughan:
Quite right, too. Don't you think that's more natural?
If by 'natural' you mean 'complete', yes. I was trying to ascertain why the counts were different for bases 2-5 & 7-8 from Jean-Paul Davalan's solution sets at the bottom of this page:
http://www.cetteadressecomportecinquantesignes.com/DixChiffres.htm
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There are none for 19 and 20. I'm beginning to believe that for n large such permutations are quite rare. Victor On Mon, Mar 5, 2012 at 5:58 PM, Victor Miller <victorsmiller@gmail.com> wrote:
17 has 10 such permutations, and 18 has exactly 1. Computational challenge: find the unique permutation of 0..17 which has the property that the product of two consecutive elements when written in base 17 (and is not 1 digit in base 17) appears somewhere in this permutation.
Victor
On Mon, Mar 5, 2012 at 5:00 PM, Victor Miller <victorsmiller@gmail.com> wrote:
Here are a few more members of the sequences (here's the whole sequence starting at 1):
1,2,6,14,20,27,68,41,29,58,20,0,18,25,0,0
Hmm. Lot's of 0's.
Victor
On Mon, Mar 5, 2012 at 9:25 AM, Hans Havermann <gladhobo@teksavvy.com> wrote:
On Monday 05 March 2012 05:23:17 Hans Havermann wrote:
Victor Miller:
I wrote a backtracking program to calculate the number of such sequences for base b=2 through 13. Here are the numbers 2,6,14,20,27,68,41,29,58,20,0,18.
I believe that you may have included in your count numbers that begin with a zero.
Gareth McCaughan:
Quite right, too. Don't you think that's more natural?
If by 'natural' you mean 'complete', yes. I was trying to ascertain why the counts were different for bases 2-5 & 7-8 from Jean-Paul Davalan's solution sets at the bottom of this page:
http://www.cetteadressecomportecinquantesignes.com/DixChiffres.htm
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Oh, my. He was a Math-Funster from the first generation, from just after Math-Fun "went public". Always thought-provoking, very fine mathematical intuition, great sense of humor. This is very sad. On Mon, Jan 2, 2012 at 3:33 PM, Thane Plambeck <tplambeck@gmail.com> wrote:
I just learned of the death of Dan Hoey last fall.
http://www.washingtonpost.com/local/obituaries/daniel-j-hoey-computer-specia...
-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/ _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
If anyone wishes to send remembrances to his widow, I'm sure they would be appreciated; email me privately for the email address to use. Of course Dan died a few months ago. -tom On Tue, Jan 3, 2012 at 1:38 PM, Allan Wechsler <acwacw@gmail.com> wrote:
Oh, my. He was a Math-Funster from the first generation, from just after Math-Fun "went public". Always thought-provoking, very fine mathematical intuition, great sense of humor. This is very sad.
On Mon, Jan 2, 2012 at 3:33 PM, Thane Plambeck <tplambeck@gmail.com> wrote:
I just learned of the death of Dan Hoey last fall.
http://www.washingtonpost.com/local/obituaries/daniel-j-hoey-computer-specia...
-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/ _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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Yeah, it seems somehow rude not to have known. If you're in frequent contact, just let her know that some math-fun old-timers remember him fondly. On Tue, Jan 3, 2012 at 4:43 PM, Tom Rokicki <rokicki@gmail.com> wrote:
If anyone wishes to send remembrances to his widow, I'm sure they would be appreciated; email me privately for the email address to use.
Of course Dan died a few months ago.
-tom
On Tue, Jan 3, 2012 at 1:38 PM, Allan Wechsler <acwacw@gmail.com> wrote:
Oh, my. He was a Math-Funster from the first generation, from just after Math-Fun "went public". Always thought-provoking, very fine mathematical intuition, great sense of humor. This is very sad.
On Mon, Jan 2, 2012 at 3:33 PM, Thane Plambeck <tplambeck@gmail.com> wrote:
I just learned of the death of Dan Hoey last fall.
http://www.washingtonpost.com/local/obituaries/daniel-j-hoey-computer-specia...
-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/ _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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participants (8)
-
Allan Wechsler -
Eric Angelini -
Gareth McCaughan -
Hans Havermann -
Neil Sloane -
Thane Plambeck -
Tom Rokicki -
Victor Miller