login
A195984
The size of the smallest boundary square in simple perfect squared rectangles of order n.
0
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
REFERENCES
Gambini, Ian. Thesis; 'Quant aux carrés carrelés' L’Universite de la Mediterranee Aix-Marseille II 1999
CROSSREFS
Cf. A002839.
Sequence in context: A273980 A101642 A269354 * A019535 A229446 A205704
KEYWORD
nonn
AUTHOR
Stuart E Anderson, Sep 26 2011
EXTENSIONS
Added a(23) = 8, Stuart E Anderson, Nov 30 2012
Added a(24) = 7, Stuart E Anderson, Dec 07 2012
STATUS
approved