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

Author

Hugo Pfoertner, Jun 01 2003

Keywords

• hard
• nonn

Comments

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

Examples

			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.
		

References

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

Links

• 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

Crossrefs

Cf. A084616, A023393, A084644.

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