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A089047 Edge length of largest square dissectable into up to n squares in Mrs. Perkins's quilt problem. 6

%I

%S 1,1,1,2,2,3,4,5,7,9,13,17,23,29,41,53,70,91,126,158,216,276,386,488,

%T 675,866,1179,1544,2136,2739,3755,4988,6443

%N Edge length of largest square dissectable into up to n squares in Mrs. Perkins's quilt problem.

%C An inverse to A005670.

%C More precisely, a(n) = greatest k such that A005670(k) <= n. - _Peter Munn_, Mar 13 2018

%C It is not clear which terms have been proved to be correct and which are just conjectures. - _Geoffrey H. Morley_, Sep 07 2012; _N. J. A. Sloane_, Jul 06 2017

%C Terms up to and including a(18) have been proved correct by Ed Wynn (2013). - _Stuart E Anderson_, Sep 16 2013

%C A089046 and A089047 are almost certainly correct up to 5000. - _Ed Pegg Jr_, Jul 06 2017

%C Deleted terms above 5000. - _N. J. A. Sloane_, Jul 06 2017

%C Further best known terms are 8568, 11357, 14877, 19594, 26697, 34632. - _Ed Pegg Jr_, Jul 06 2017

%C A290821 is the equivalent sequence for equilateral triangles. - _Peter Munn_, Mar 06 2018

%H Ed Pegg, Jr., <a href="http://www.mathpuzzle.com/perkinsbestquilts.txt">Mrs. Perkins's Quilts</a>

%H Ed Pegg Jr. and Richard K. Guy, <a href="http://demonstrations.wolfram.com/MrsPerkinssQuilts/">Mrs. Perkins's Quilts</a> (Wolfram Demonstrations Project)

%H Ed Wynn, <a href="http://arxiv.org/abs/1308.5420">Exhaustive generation of Mrs Perkins's quilt square dissections for low orders</a>, arXiv:1308.5420 [math.CO], 2013-2014.

%Y Cf. A005670, A014529, A018835, A089046, A211302, A290821.

%K nonn,hard,more

%O 1,4

%A _R. K. Guy_, Dec 03 2003

%E More terms from _Ed Pegg Jr_, Dec 03 2003

%E Corrected and extended by _Ed Pegg Jr_, Apr 18 2010

%E Duplicate a(6) deleted and a(22)-a(26) revised (from _Ed Pegg Jr_, Jun 15 2010) by _Geoffrey H. Morley_, Sep 07 2012

%E Conjectured terms have been extended up to a(44), based on simple squared square enumeration, by Duijvestijn, Skinner, Anderson, Pegg, Johnson, Milla and Williams. - _Stuart E Anderson_, Sep 16 2013

%E a(33) and further terms added by _Ed Pegg Jr_, Jul 06 2017

%E Name edited by _Peter Munn_, Mar 14 2018

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Last modified September 20 22:20 EDT 2018. Contains 315247 sequences. (Running on oeis4.)