A376066 Minimum number of unit squares needed to cover the circumference of a circle of radius n.

4, 9, 14, 18, 23, 27, 32, 36, 40, 45, 49, 54, 58, 63, 67, 72, 76, 80, 85, 89, 94, 98, 103, 107, 112, 116, 120, 125, 129, 134, 138, 143, 147, 152, 156, 160, 165, 169, 174, 178, 183, 187, 192, 196, 200, 205, 209, 214, 218, 223, 227, 232, 236, 240, 245, 249, 254, 258, 263, 267, 272, 276, 280, 285, 289, 294, 298, 303, 307, 311

Offset: 1

Author

Maurice Clerc, Sep 08 2024

Keywords

• easy
• nonn

Comments

For n>=2, a unit square covers the most circumference when it has two diagonally opposite corners on the circumference, forming a chord of length sqrt(2).

A simple upper bound a(n) <= u(n) = ceiling(2*Pi*n/sqrt(2)) would be by sqrt(2) arcs instead of chords, and which is bigger at for instance a(70) = 311 < u(70) = 312 (see A376207).

Crossrefs

Cf. A376207.

Formula

a(n) = ceiling(Pi/arcsin(sqrt(2)/(2*n))).