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A089046
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Least edge-length of a square dissectable into at least n squares in the Mrs. Perkins's quilt problem.
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4
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1, 2, 2, 2, 3, 3, 4, 5, 6, 8, 10, 14, 18, 24, 30, 40, 54, 71, 92, 121, 155, 210, 266, 360, 476, 642, 833, 1117, 1485, 1967, 2595, 3465, 4534, 5995
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OFFSET
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1,2
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COMMENTS
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n <= 15 (and possibly 16) proved minimal by J. H. Conway (Conway, J. H. "Re: [math-fun] Mrs. Perkins Quilt - Orders 89, 90 improved over UPIG." math-fun mailing list. October 10, 2003.). The conjectures are best currently known values of a(n) for n > 16. - Stuart E Anderson, Apr 21 2013
Upper bounds for the next terms in the sequence (which may well be the true values) are 7907, 10293, 13505, 17785, 23239, 31035, 39571, ... - Ed Pegg Jr, Jul 06 2017
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REFERENCES
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H. T. Croft, K. J. Falconer, and R. K. Guy, Section C3 in Unsolved Problems in Geometry, New York: Springer, 1991.
M. Gardner, "Mrs. Perkins's Quilt and Other Square-Packing Problems," Mathematical Carnival, New York: Vintage, 1977.
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LINKS
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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Confirmed a(30) as best known, added a(31) as best known. - Stuart E Anderson, Apr 21 2013
Using James Williams recent discoveries of 15 million simple perfect squared squares in orders 31 to 44 I was able to extend the sequence of best currently known values for optimal quilts from a(32) to a(44). - Stuart E Anderson, Apr 21 2013
Using Anderson and Milla's enumeration of order 31 and 32 perfect squared squares, improved conjectures for a(32) and a(33) were obtained - Stuart E Anderson, Sep 16 2013
a(29) corrected and further terms added by Ed Pegg Jr, Jul 06 2017
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STATUS
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approved
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