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

1,1

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).

Links

Table of n, a(n) for n=1..70.

Formula

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

Crossrefs

Cf. A376207.

Sequence in context: A313042 A313043 A313044 * A313045 A313046 A313047

Adjacent sequences: A376063 A376064 A376065 * A376067 A376068 A376069

Keyword

easy,nonn

Author

Maurice Clerc, Sep 08 2024

Status

approved