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| A286312
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Table read by antidiagonals upwards: a(n, k) is the minimum c such that n sets with k elements each can be constructed from numbers 1 to c (inclusive) such that any two sets have exactly 1 common element.
(history;
published version)
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#12 by N. J. A. Sloane at Tue May 16 00:13:45 EDT 2017
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#11 by Wesley Ivan Hurt at Tue May 09 21:49:11 EDT 2017
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Discussion
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| Mon May 15
| 08:04
| Andrey Zabolotskiy: I can prove that a(2(k-1),k) <= (k-1)^2+2 and a(3(k-1),k) <= (k-1)^2+3, and also a(3k-2,k) <= k^2-k+1 except at k=2. Also, a(n,k) <= a(n,k-1)+n. I'll add this to the discussion at StackExchange later, and maybe I'll manage to find some generalization.
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| 09:18
| Andrey Zabolotskiy: Oh, and JeanMarie at StackOverflow brings the really basic statement: a(p^2+p+1, p+1) = p^2+p+1 for prime p, if I understand him correctly.
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#10 by Wesley Ivan Hurt at Tue May 09 21:49:08 EDT 2017
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| NAME
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Table read by antidiagonals upwards: a(n, k) is the minimum c such that n sets with k elements each can be constructed from numbers 1 to c (inclusive) such that any two sets have exactly 1 common element.
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| FORMULA
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n< < k+2: a(n,k)=) = kn-(n(n-1))/2.
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| STATUS
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proposed
editing
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#9 by Simon Bohnen at Mon May 08 09:52:47 EDT 2017
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#8 by Simon Bohnen at Mon May 08 09:49:49 EDT 2017
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| FORMULA
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n<k+2: a(n,k)=kn-(n(n-1))/2.
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| STATUS
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proposed
editing
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Discussion
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| Mon May 08
| 09:50
| Simon Bohnen: Of course it has to be a(n,k).
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#7 by Michel Marcus at Sun May 07 07:23:49 EDT 2017
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Discussion
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| Mon May 08
| 08:23
| Michel Marcus: Formula: rather ? a(n,k) = kn-(n(n-1))/2 for n< k+2
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#6 by Michel Marcus at Sun May 07 07:22:58 EDT 2017
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| EXTENSIONS
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Added authors to the links, Simon Bohnen, May 06 2017
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| STATUS
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proposed
editing
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Discussion
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| Sun May 07
| 07:23
| Michel Marcus: No extensions needed at this stage before sequence is approved
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#5 by Simon Bohnen at Sun May 07 07:19:09 EDT 2017
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#4 by Simon Bohnen at Sat May 06 06:37:05 EDT 2017
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| LINKS
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<Simon Bohnen, <a href="https://github.com/Simonibo/dobble-generate/blob/master/values.xlsx">Extended table of values</a>
<Simon Bohnen, <a href="https://github.com/Simonibo/dobble-generate/tree/master/src">A Java program for generating the sequence</a>
<Simon Bohnen and other users, <a href="https://math.stackexchange.com/questions/2216585/what-is-the-minimal-number-of-different-symbols-in-the-game-dobble">Further discussion and proof for the formula</a>
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| EXTENSIONS
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Added authors to the links, Simon Bohnen, May 06 2017
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| STATUS
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proposed
editing
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#3 by Simon Bohnen at Sat May 06 06:08:07 EDT 2017
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Discussion
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| Sat May 06
| 06:22
| Michel Marcus: Please the links should be like Author, <a href="http://www.etc.etc/file">Title</a> see https://oeis.org/eishelp2.html#RH and existing sequences
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