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

Author

Stuart E Anderson, Sep 26 2011

Keywords

• nonn

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

References

• Gambini, Ian. Thesis; 'Quant aux carrés carrelés' L’Universite de la Mediterranee Aix-Marseille II 1999

Links

• 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

Crossrefs

Cf. A002839.

Extensions

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

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