A195984 The size of the smallest boundary square in simple perfect squared rectangles of order n.

8, 13, 22, 18, 14, 13, 11, 9, 6, 9, 7, 7, 8, 6, 8, 7

Offset

9,1

Comments

Ian Gambini showed in his thesis that the minimum value for a(n) is 5. Brian Trial found 3 simple perfect squared rectangles (SPSRs) of order 28 with boundary squares of size 5 in September 2011. An unsolved problem is to find the lowest order SPSR with a '5 on the side'.

Added a(22) = 6 (Stuart Anderson), Brian Trial has found a(28) = 5. This gives an upper bound of 28, in addition to the lower bound of 23, to the problem of finding the lowest order SPSR with a square of size 5 on the boundary. - Stuart E Anderson, Sep 29 2011

Found a(23) = 8, the lower bound is now order 24. - Stuart E Anderson, Nov 30 2012

Found a(24) = 7, the lower bound is now order 25. - Stuart E Anderson, Dec 07 2012

Links

Table of n, a(n) for n=9..24.

Stuart E. Anderson, Simple Perfects by Boundary Rules and Conditions.

Stuart Anderson, 'Special' Perfect Squared Squares, accessed 2014. - N. J. A. Sloane, Mar 30 2014

Ian Gambini, Quant aux carrés carrelés, Thesis, Université de la Méditerranée Aix-Marseille II, 1999.

Crossrefs

Cf. A002839.

Sequence in context: A273980 A101642 A269354 * A019535 A229446 A205704

Adjacent sequences: A195981 A195982 A195983 * A195985 A195986 A195987

Keyword

nonn,more

Author

Stuart E Anderson, Sep 26 2011

Extensions

a(23) = 8 added by Stuart E Anderson, Nov 30 2012

a(24) = 7 added by Stuart E Anderson, Dec 07 2012

Status

approved