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

2, 3, 4, 7, 19, 37, 55, 85, 121, 147, 148, 150, 151, 187, 188, 190, 191, 192, 193, 198, 199, 235, 241, 264, 267, 269, 270, 291, 292, 293, 294, 295, 343, 346, 347, 348, 349, 408, 409, 412, 414, 415, 417, 418, 419, 420, 421, 481, 499, 564, 565, 649, 689, 690, 721

Offset: 1

Author

Hugo Pfoertner, Jun 01 2003

Keywords

• nonn

Comments

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.

Examples

			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.
		

References

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

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..85
• Jerry Donovan, Packing Circles in Squares and Circles Page.
• Hugo Pfoertner, Minimum area of circle needed to cover n circles of area 1
• E. Specht, The best known packings of equal circles in the unit circle
• E. Specht, The sequence of N's that establish density records - provides continuation of the sequence.

Crossrefs

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

Extensions

More terms from Robert G. Wilson v, Nov 07 2012