A018835 -id:A018835 - cp's OEIS frontend

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

1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 13, 17, 23, 29, 41, 53, 70, 91, 126, 158, 216, 276, 386, 488, 675, 866, 1179, 1544, 2136, 2739, 3755, 4988, 6443

Offset: 1

R. K. Guy, Dec 03 2003

An inverse to A005670.
More precisely, a(n) = greatest k such that A005670(k) <= n. - Peter Munn, Mar 13 2018
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
Terms up to and including a(18) have been proved correct by Ed Wynn (2013). - Stuart E Anderson, Sep 16 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
Further best known terms are 8568, 11357, 14877, 19594, 26697, 34632. - Ed Pegg Jr, Jul 06 2017
A290821 is the equivalent sequence for equilateral triangles. - Peter Munn, Mar 06 2018

Ed Pegg, Jr., Mrs. Perkins's Quilts
Ed Pegg Jr. and Richard K. Guy, Mrs. Perkins's Quilts (Wolfram Demonstrations Project)
Ed Wynn, Exhaustive generation of Mrs Perkins's quilt square dissections for low orders, arXiv:1308.5420 [math.CO], 2013-2014.

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

More terms from Ed Pegg Jr, Dec 03 2003
Corrected and extended by Ed Pegg Jr, Apr 18 2010
Duplicate a(6) deleted and a(22)-a(26) revised (from Ed Pegg Jr, Jun 15 2010) by Geoffrey H. Morley, Sep 07 2012
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
a(33) and further terms added by Ed Pegg Jr, Jul 06 2017
Name edited by Peter Munn, Mar 14 2018

A211302 Minimal number of smaller integer-sided squares that tile a p X p square, where p = n-th prime.

Original entry on oeis.org

4, 6, 8, 9, 11, 11, 12, 13, 13, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19

Offset: 1

N. J. A. Sloane, Apr 07 2012

Sasha Kurz, Squaring the square with integer linear programming.
Ed Wynn, Exhaustive generation of Mrs Perkins's quilt square dissections for low orders, arXiv:1308.5420 [math.CO], 2013.

Cf. A000040, A018835.

More terms from Wynn, 2013. - N. J. A. Sloane, Nov 29 2013

A340919 Sorted sizes of the 55 squares used in the first known squared square of dimension 4205 X 4205 found by Roland Sprague in 1938.

Original entry on oeis.org

13, 29, 35, 39, 50, 52, 65, 78, 87, 91, 104, 116, 117, 130, 140, 143, 145, 174, 182, 195, 203, 221, 232, 234, 247, 261, 270, 286, 290, 299, 305, 312, 319, 325, 340, 375, 406, 429, 435, 493, 522, 551, 565, 575, 615, 638, 665, 667, 696, 705, 725, 957, 1040, 1885, 2320

Offset: 1

Hugo Pfoertner, Feb 16 2021

Stuart Anderson, Roland Percival Sprague (1894-1967), history and bibliography on squaring.net.
James Grime, A Nice Square, Numberphile video, 2017.
David Moews, Squared rectangles, 2007 (provides Bouwcamp code of square).
Roland P. Sprague, Beispiel einer Zerlegung des Quadrats in lauter verschiedene Quadrate, Mathematische Zeitschrift, 45, 607-608, 1939.
R. Sprague, An example of a dissection of the square into pairwise unequal squares, English translation.

Cf. A005670, A006983, A014530, A018835, A089047.

Sum_{k=1..55} a(k)^2 = 4205^2.

cp's OEIS Frontend

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

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A211302 Minimal number of smaller integer-sided squares that tile a p X p square, where p = n-th prime.

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A340919 Sorted sizes of the 55 squares used in the first known squared square of dimension 4205 X 4205 found by Roland Sprague in 1938.

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