[math-fun] A true Mac Mahon ruler?
Hello Math-Fun (posted here as SeqFans didn't publish my mail) The first 8 terms of A002049 are: 1,3,7,12,20,30,44 and 59. I see that I can measure 29 in two ways with this ruler (I thought only one way was authorized): 30-1=29 59-30=29 I am obviously missing smthg as this is an ancient seq. signed by Neil himself. Anyway -- is it possible to build a wooden ruler with as few as possible vertical marks such that all integers measures between 1 and 200 can be materialized only once? I guess this sort of question is as old as the hat I'm wearing right now to avoid the killer sun we currently have in Brussels. Forgive me. Best, É.
If you require all differences to be unique, then you're looking for a Golomb ruler. If you require all differences to be unique *and* you want to measure all values 1..200, then you're looking for a perfect Golomb ruler. There are no perfect Golomb rulers with more than five marks (measuring distances 1..11). On Tue, Jun 25, 2019 at 11:22 AM Éric Angelini <eric.angelini@skynet.be> wrote:
Hello Math-Fun (posted here as SeqFans didn't publish my mail) The first 8 terms of A002049 are: 1,3,7,12,20,30,44 and 59. I see that I can measure 29 in two ways with this ruler (I thought only one way was authorized): 30-1=29 59-30=29 I am obviously missing smthg as this is an ancient seq. signed by Neil himself. Anyway -- is it possible to build a wooden ruler with as few as possible vertical marks such that all integers measures between 1 and 200 can be materialized only once? I guess this sort of question is as old as the hat I'm wearing right now to avoid the killer sun we currently have in Brussels. Forgive me. Best, É.
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Thanks very much, Tomas and Kerry -- this is clear now! Best, É.
Le 25 juin 2019 à 21:26, Tomas Rokicki <rokicki@gmail.com> a écrit :
If you require all differences to be unique, then you're looking for a Golomb ruler. If you require all differences to be unique *and* you want to measure all values 1..200, then you're looking for a perfect Golomb ruler. There are no perfect Golomb rulers with more than five marks (measuring distances 1..11).
On Tue, Jun 25, 2019 at 11:22 AM Éric Angelini <eric.angelini@skynet.be> wrote:
Hello Math-Fun (posted here as SeqFans didn't publish my mail) The first 8 terms of A002049 are: 1,3,7,12,20,30,44 and 59. I see that I can measure 29 in two ways with this ruler (I thought only one way was authorized): 30-1=29 59-30=29 I am obviously missing smthg as this is an ancient seq. signed by Neil himself. Anyway -- is it possible to build a wooden ruler with as few as possible vertical marks such that all integers measures between 1 and 200 can be materialized only once? I guess this sort of question is as old as the hat I'm wearing right now to avoid the killer sun we currently have in Brussels. Forgive me. Best, É.
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On Tue, Jun 25, 2019 at 8:22 PM Éric Angelini <eric.angelini@skynet.be> wrote:
Hello Math-Fun (posted here as SeqFans didn't publish my mail)
Dear Eric, "seqfan" did post your mail, but you are not in copy (that's a feature, not a bug). You have already received answers as I write this. Cheers, Olivier
The answer to my question was (of course) already in the OEIS: https://oeis.org/A247556 BTW, this seq is not at all OBSC (keyword). It should be labelled BEAU(tiful) instead! Best, É.
Le 25 juin 2019 à 20:21, Éric Angelini <eric.angelini@skynet.be> a écrit : Hello Math-Fun (...) Anyway -- is it possible to build a wooden ruler with as few as possible vertical marks such that all integers measures between 1 and 200 can be materialized only once? (...)
Hello Math-Fun (Xpost to SeqFan), Here is a strange sequence just submitted: https://oeis.org/A309151 It says: Lexicographically earliest sequence of distinct terms starting with a(1) = 1 such that a(n) doesn't share any digit with the cumulative sum a(1) + a(2) + a(3) + ... + a(n-1) + a(n). And in the Comments section: As this sequence needs a lot of backtracking, we don't guarantee the accuracy of the last 79 integers of the 1079-term b-file. Indeed, the problem comes from the fact that some cumulative sums quickly block the extension of the sequence. This is the case with 10 (or any other sum ending in zero). But this is the case too with 301 after 1,2,3,5,4,6,7,8,9,10,11,12,14,22,20,23,24,30,13,15,16,18,28. So, we bumped quite often in a "bad sum" (on the average, the sequence was extended by 100 terms for every backtrack). To make a prior list of "bad sums" is difficult (meaning impossible, I guess): 258002 is such a "bad sum" if you have previously used {1,3,4,6,7,9,39,49,69,79} else 258002 + 79 = 258081 would be ok. So my questions are: could the sequence be infinite? Could a list of "bad sum numbers" be easely defined and used? Best, É.
https://oeis.org/A309151 EA: "As this sequence needs a lot of backtracking, we don't guarantee the accuracy of the last 79 integers of the 1079-term b-file." This (and the fact that Neil approved it) surprises me since the OEIS style sheet suggests that (for sequences with conjectured terms) "we give the known terms (up to the first gap) in a b-file, and all the terms - with gaps, question marks, or ranges for the uncertain terms - in an a-file".
Hans, They claim that 1000 terms of the 1079-term b-file are correct, and imply that the remaining 79 terms are too. So I approved it, hoping that someone like you would check it when they saw that comment. Furthermore, this is a member of the class of "lexicographically earliest sequences" , of which we have a large number in the OEIS, and there is no mystery about them. Backtracking is all it takes. Nothing deep here. Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com On Sun, Jul 14, 2019 at 9:58 PM Hans Havermann <gladhobo@bell.net> wrote:
EA: "As this sequence needs a lot of backtracking, we don't guarantee the accuracy of the last 79 integers of the 1079-term b-file."
This (and the fact that Neil approved it) surprises me since the OEIS style sheet suggests that (for sequences with conjectured terms) "we give the known terms (up to the first gap) in a b-file, and all the terms - with gaps, question marks, or ranges for the uncertain terms - in an a-file". _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
"Nothing deep here" I said, referring to the class of "lexicographically earliest sequences". I take it back. A282317, the lex. earliest cube-free binary sequence, needed an argument from topology to show that it exists. So A309151 may not be so trivial. The present definition of A309151 is "Lexicographically earliest sequence of distinct terms starting with a(1) = 1 such that a(n) doesn't share any digit with the cumulative sum a(1) + a(2) + a(3) + ... + a(n-1) + a(n)" But this is the finite sequence 1,2,3,4, no? It can't be extended! It satisfies the conditions, and any other sequence satisfying the conditions must start 1,2,3,m with m >= 5. Maybe the authors should modify the definition to say "Lexicographically earliest infinite sequence of distinct terms starting with a(1) = 1 such that a(n) doesn't share any digit with the cumulative sum a(1) + a(2) + a(3) + ... + a(n-1) + a(n)."? But then we don't know how many of the present terms are correct! I'm sending the sequence back to the editing stack. On Sun, Jul 14, 2019 at 10:14 PM Neil Sloane <njasloane@gmail.com> wrote:
Hans, They claim that 1000 terms of the 1079-term b-file are correct, and imply that the remaining 79 terms are too. So I approved it, hoping that someone like you would check it when they saw that comment.
Furthermore, this is a member of the class of "lexicographically earliest sequences" , of which we have a large number in the OEIS, and there is no mystery about them. Backtracking is all it takes. Nothing deep here.
Best regards Neil
Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com
On Sun, Jul 14, 2019 at 9:58 PM Hans Havermann <gladhobo@bell.net> wrote:
EA: "As this sequence needs a lot of backtracking, we don't guarantee the accuracy of the last 79 integers of the 1079-term b-file."
This (and the fact that Neil approved it) surprises me since the OEIS style sheet suggests that (for sequences with conjectured terms) "we give the known terms (up to the first gap) in a b-file, and all the terms - with gaps, question marks, or ranges for the uncertain terms - in an a-file". _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (6)
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Hans Havermann -
Neil Sloane -
Olivier Gerard -
Tomas Rokicki -
Éric Angelini -
Éric Angelini