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A084644 Best packings of m>1 equal circles into a larger circle setting a new density record. 4


%S 2,3,4,7,19,37,55,85,121,147,148,150,151,187,188,190,191,192,193,198,

%T 199,235,241,264,267,269,270,291,292,293,294,295,343,346,347,348,349,

%U 408,409,412,414,415,417,418,419,420,421,481,499,564,565,649,689,690,721

%N Best packings of m>1 equal circles into a larger circle setting a new density record.

%C Sequence terms for n>5 are only conjectures. The arrangement of 37 circles consists of one central circle surrounded by 3 rings of 6,12 and 18 circles. For n=7, 49 of the 55 circles are arranged in a rigid hexagonal lattice with 6 "rattlers" inserted in gaps at the circumference.

%D List of references given by E. Specht; see corresponding link.

%H Robert G. Wilson v, <a href="/A084644/b084644.txt">Table of n, a(n) for n = 1..85</a>

%H Jerry Donovan, <a href="http://web.archive.org/web/20040216031401/http://home.att.net/~donovanhse/Packing/index.html">Packing Circles in Squares and Circles Page.</a>

%H Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/a084618.pdf">Minimum area of circle needed to cover n circles of area 1</a>

%H E. Specht, <a href="http://hydra.nat.uni-magdeburg.de/packing/cci/cci.html">The best known packings of equal circles in the unit circle</a>

%H E. Specht, <a href="http://hydra.nat.uni-magdeburg.de/packing/cci/txt/records.txt">The sequence of N's that establish density records</a> - provides continuation of the sequence.

%e a(4)=7 because the density 0.7777.. of the best packing of 7 circles (1 central circle surrounded by 6 neighbors) exceeds the density 0.68629.. of the packing of 4 circles arranged in a square.

%Y Cf. A051657 (density records for circles packed into square), A084618, A023393.

%K nonn

%O 1,1

%A _Hugo Pfoertner_, Jun 01 2003

%E More terms from _Robert G. Wilson v_, Nov 07 2012

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Last modified November 21 06:00 EST 2019. Contains 329350 sequences. (Running on oeis4.)