Re Challenge sequences

[N. J. A. Sloane]

Thanks to all the seqfans who replied.

Here is the list that I sent to those people.  The idea is
that hopefully they will choose one, and then they will all work on it.

I will let the list know if anything significant happens!

Neil

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Suggestion #1:

From: "Rainer Rosenthal" <r.rosenthal at 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 :-)

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Suggestion #2:

From: Don Reble <djr at nk.ca>

I suggest A006945, although it does not satisfy all of
the conditions that were listed.

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From: "Pfoertner, Hugo" <Hugo.Pfoertner at 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

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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

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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

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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.

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Suggestion #7:

From: Ralf Stephan <ralf at 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)

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Suggestion #8:

From: Ed Pegg Jr <edp at 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

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