To math-fun, I was asked by a group of programmers in France to suggest a sequence that they could attack as a team effort. They imposed several conditions that I found hard to satisfy, so I asked the sequence-fan mailing list for help. This resulted in the following list of "challenge sequences", which I sent to France, and post here just for fun. Presumably these people will select one of them to work on. NJAS ------------------------------------------------------- Suggestion #1: From: "Rainer Rosenthal" <r.rosenthal@web.de> In the German newsgroup de.sci.mathematik we discussed "Perfect Rulers" and there were some enhancements for http://www.research.att.com/projects/OEIS?Anum=A004137 some weeks ago. Let them compute A004137(n) from scratch. They will enjoy (I hope). And the OEIS will be glad :-) ----------------------------------------------------------- Suggestion #2: From: Don Reble <djr@nk.ca> I suggest A006945, although it does not satisfy all of the conditions that were listed. ----------------------------------------------------------- From: "Pfoertner, Hugo" <Hugo.Pfoertner@muc.mtu.de> Suggestion #3: Confirm Daren Casella's results for The Snake or Coil in the Box Problem: http://www.research.att.com/projects/OEIS?Anum=A000937 2,4,6,8,14,26,48 Name: Length of longest simple cycle without chords in the n-dimensional hypercube graph. Also called n-coil or closed n-snake-in-the-box problem. After 48, lower bounds on the next terms are 96,180,344,630,1236. - Darren Casella (artdeco42(AT)yahoo.com), Mar 04 2005 http://www.research.att.com/projects/OEIS?Anum=A099155 Sequence: 1,2,4,7,13,26,50 Name: Maximum length of a simple path with no chords in the n-dimensional hypercube, also known as snake-in-the-box problem. After 50, lower bounds on the next terms are 97,186,358,680,1260. - Darren Casella (artdeco42(AT)yahoo.com), Mar 04 2005 ----------- Suggestion #4: Find an extension of http://www.research.att.com/projects/OEIS?Anum=A087725 Sequence: 0,6,31,80 Name: Maximum number of moves required for the n X n generalization of Sam Loyd's Fifteen Puzzle. As a "warm-up" for this the research group could complete http://www.research.att.com/projects/OEIS?Anum=A089484 Sequence: 1,2,4,10,24,54,107,212,446,946,1948,3938,7808,15544,30821, 60842,119000,231844,447342,859744 Name: Number of configurations of Sam Loyd's sliding block 15-puzzle that require a minimum of n moves to be reached, starting with the empty square in one of the corners. and the related http://www.research.att.com/projects/OEIS?Anum=A090164 and http://www.research.att.com/projects/OEIS?Anum=A090165 ----------- Suggestion #5: http://www.research.att.com/projects/OEIS?Anum=A085000 Sequence: 1,10,412,40800,6839492,1865999570 Name: Maximal determinant of an n X n matrix using the integers 1 to n^2. I have spent more than 2 years of CPU time to get a current lower bound for a(7)>=762140212575 and much less time for a(8)>=440857916120379 ------------ Suggestion #6: Similar problems dealing with the spectrum of determinants: http://www.research.att.com/projects/OEIS?Anum=A089472 Sequence: 2,3,5,7,11,19,43 Name: Number of different values taken by the determinant of a real (0,1)-matrix of order n. and some of the sequences cross-linked in A089472. -------------------------------------------------------- Suggestion #7: From: Ralf Stephan <ralf@ark.in-berlin.de> Permanents of matrices would be a good choice. For example, A087983. (There are many related sequences that need extending and have not been studied hardly at all. Search for the word permanent in the OEIS) -------------------------------------------------------- Suggestion #8: From: Ed Pegg Jr <edp@wolfram.com> ID Number: A081287 URL: http://www.research.att.com/projects/OEIS?Anum=A081287 Sequence: 0,1,1,5,5,8,14,6,15,20,7,17,17,20,25,16,9,30,21,20,33 Name: Excess area when consecutive squares of size 1 to n are packed into the smallest possible rectangle. References R. M. Kurchan (editor), Puzzle Fun, Number 18 (December 1997), pp. 9-10. Links: Ed Pegg Jr, Packing squares http://www.maa.org/editorial/mathgames/mathgames_12_01_03.html See also: Cf. A038666. Does it ever go back down to zero? I'll pay $100 for a solution to that. The best known solution for 1-24 is http://www.mathpuzzle.com/24sqB.gif ------------------------------------------------------------------