cp's OEIS Frontend

A247397 Numbers n such that when n unit-diameter circles are arranged non-overlapping in the plane, and those circles are then enclosed in a rectangle, the area of the rectangle must be at least n.

%I A247397 #17 Jul 29 2015 12:12:37
%S A247397 1,2,3,4,5,6,7,8,9,10,12,13
%N A247397 Numbers n such that when n unit-diameter circles are arranged non-overlapping in the plane, and those circles are then enclosed in a rectangle, the area of the rectangle must be at least n.
%C A247397 For any number that does not appear on this list, there exists an arrangement of that number of unit-diameter circles that can be enclosed in a rectangle with area of less than 1 square unit per circle.
%C A247397 Any number of unit-diameter circles greater than or equal to 14 can be arranged in two rows, where the upper row is offset by 1/2 horizontally and (sqrt(3/4)-1) vertically, thereby reducing the minimum size of the enclosing rectangle to less than n square units. However, this isn't necessarily the overall minimum.
%C A247397 In addition, 11 unit-diameter circles placed in 3 rows can be enclosed in an area less than 11 square units.
%H A247397 Eckard Specht, <a href="http://hydra.nat.uni-magdeburg.de/packing/crc_var/crc.html">Densest known packings of a given number of circles in a rectangle</a>
%e A247397 11 unit-diameter circles can be placed in a hexagonal array, with rows of 4, 3 and 4 circles in respective rows, which can be enclosed in a rectangle 4 units wide and (1+sqrt(3)) high, giving an area of 10.93, less than 11 square units. Any fewer circles than this, and also 12 or 13 circles, cannot be enclosed in a rectangle smaller than n square units in area.
%K A247397 nonn,fini,full
%O A247397 1,2
%A A247397 _Elliott Line_, Sep 16 2014