

A005842


a(n) = minimal integer m such that an m X m square contains nonoverlapping squares of sides 1, ..., n (some values are only conjectures).
(Formerly M2401)


3



1, 3, 5, 7, 9, 11, 13, 15, 18, 21, 24, 27, 30, 33, 36, 39, 43, 47, 50, 54, 58, 62, 66, 71, 75, 80, 84, 89, 93, 98, 103, 108, 113, 118, 123, 128, 133, 139, 144, 150, 155, 161, 166, 172, 178, 184, 190, 196, 202, 208, 214, 221, 227, 233, 240, 246
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OFFSET

1,2


COMMENTS

The entries for n=1, 2, 8, 15, 16, 17, 19, 20, 21, 22, 23, 25, 27, 29, 30, 31, 35, 36, 37, 39, 41, 43, 44, 45, 46, 49, 50, 51, 54, and 56 all meet the lower bound in A092137 and are therefore correct.  Stuart E Anderson, Jan 05 2008
Simonis, H. and O'Sullivan showed that a(26) = 80.  Erich Friedman, May 27 2009
Houhardy S. showed a(32)=108, a(33)=113, a(34)=118, and a(47)=190.  Erich Friedman, Oct 11 2010
The values have been proved correct except those for n=38, 40, 42, 48, 52, 53 and 55, where they remain probable.  Erich Friedman, Oct 11 2010


REFERENCES

H. T. Croft, K. J. Falconer and R. K. Guy, Unsolved Problems in Geometry, D5.
M. Gardner, Mathematical Carnival. Random House, NY, 1977, p. 147.
Simonis, H. and O'Sullivan, B., Search Strategies for Rectangle Packing, in Proceedings of the 14th international conference on Principles and Practice of Constraint Programming, SpringerVerlag Berlin, Heidelberg, 2008, pp. 5266.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS



CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



