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A089046 Least edge-length of a square dissectable into at least n squares in the Mrs. Perkins's quilt problem. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
An inverse to A005670.
More precisely, a(n) = least k such that A005670(k) >= n. - Peter Munn, Mar 14 2018
It is not clear which terms have been proved to be correct and which are just conjectures. - Geoffrey H. Morley, Aug 29 2012; N. J. A. Sloane, Jul 06 2017
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
A089046 and A089047 are almost certainly correct up to 5000. - Ed Pegg Jr, Jul 06 2017
Deleted terms above 5000. - N. J. A. Sloane, Jul 06 2017
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
REFERENCES
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.
LINKS
Stuart E. Anderson, Mrs Perkins's Quilts
J. H. Conway, Mrs. Perkins's Quilt, Proc. Cambridge Phil. Soc. 60, 363-368, 1964.
Ed Pegg, Jr., Mrs. Perkin's Quilts
Ed Pegg Jr., Richard K. Guy, Mrs. Perkins's Quilts (Wolfram Demonstrations Project)
Ed Pegg Jr., Richard K. Guy, Mrs. Perkins's Quilts Notebook source code
G. B. Trustrum, Mrs. Perkins's Quilt, Proc. Cambridge Phil. Soc. 61, 7-11, 1965.
Eric W. Weisstein's World of Mathematics, Mrs. Perkins's Quilt
CROSSREFS
Sequence in context: A016085 A018122 A074732 * A054911 A367215 A137267
KEYWORD
nonn,hard,more
AUTHOR
R. K. Guy, Dec 03 2003
EXTENSIONS
More terms from Ed Pegg Jr, Dec 03 2003
Corrected and extended by Ed Pegg Jr, Apr 18 2010
a(24)-a(27) (from Ed Pegg Jr, Jun 15 2010) added by Geoffrey H. Morley, Aug 29 2012
a(28)-a(30) from Stuart E Anderson, Nov 22 2012
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(1)-a(19) confirmed by Ed Wynn, 2013. - N. J. A. Sloane, Nov 29 2013
a(29) corrected and further terms added by Ed Pegg Jr, Jul 06 2017
STATUS
approved

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Last modified April 16 22:11 EDT 2024. Contains 371755 sequences. (Running on oeis4.)