A084618 Maximum number of circles of area 1 that can be packed in a circle of area n.

1, 1, 1, 2, 3, 4, 4, 5, 7, 7, 8, 8, 8, 9, 10, 11, 12, 13, 14, 14, 15, 16, 17, 19, 19, 19, 20, 21, 21, 22, 23, 24, 24, 26, 27, 27, 28, 29, 30, 31, 31, 32, 33, 34, 35, 37, 37, 37, 38, 39, 40, 40, 41, 42, 42, 43, 44, 45, 46, 47, 48, 48, 49, 50, 51, 52, 53, 55, 55, 55, 56, 57, 58, 59

Offset

1,4

Comments

For most values of n these are only conjectures, supported by numerical results.

References

For list of references given by E. Specht, see corresponding link.

Links

Table of n, a(n) for n=1..74.

Erich Friedman, Circles in Circles

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

Example

a(4)=2 because a circle of area 4 is the smallest one covering two circles of area 1.
a(9)=7 is the arrangement of 6 circles closely packed around another circle. This arrangement fits into a circle that has 3*radius of smaller circles and thus 9*their area.

Crossrefs

Cf. A084616, A023393, A084644.

Equivalent sequences for packing into a square: A337020, and equilateral triangle: A337019.

Sequence in context: A330264 A356208 A036416 * A075518 A226429 A036820

Adjacent sequences: A084615 A084616 A084617 * A084619 A084620 A084621

Keyword

hard,nonn

Author

Hugo Pfoertner, Jun 01 2003.

Status

approved