A355184 Decimal expansion of the perimeter of the region that represents the set of points in a unit square that are closer to the center of the square than to the closest edge.

1, 7, 0, 3, 0, 8, 2, 4, 9, 6, 6, 5, 8, 9, 5, 3, 2, 2, 7, 8, 3, 5, 8, 4, 9, 1, 2, 2, 7, 4, 9, 2, 0, 3, 1, 5, 7, 1, 9, 8, 0, 3, 4, 4, 2, 2, 9, 5, 0, 4, 9, 7, 7, 1, 2, 1, 2, 1, 6, 6, 0, 3, 7, 8, 4, 2, 1, 7, 2, 6, 9, 2, 4, 5, 5, 2, 3, 3, 5, 0, 4, 9, 0, 3, 5, 1, 6, 3, 3, 3, 3, 1, 2, 3, 5, 3, 4, 0, 2, 3, 8, 9, 5, 7, 0

Offset

1,2

Comments

The shape is formed by the intersection of four parabolas. Its area is given in A355183.

Links

Table of n, a(n) for n=1..105.

Amiram Eldar, Illustration.

Missouri State University, Problem #5, The Area and Perimeter of a Certain Region, Advanced Problem Archive; Solution to Problem #5, by John Shonder.

Formula

Equals 2*log(sqrt(4-2*sqrt(2))+sqrt(2)-1) - sqrt(16-8*sqrt(2)) + sqrt(32-16*sqrt(2)).

Example

1.70308249665895322783584912274920315719803442295049...

Mathematica

RealDigits[2*Log[Sqrt[4 - 2*Sqrt[2]] + Sqrt[2] - 1] - Sqrt[16 - 8*Sqrt[2]] + Sqrt[32 - 16*Sqrt[2]], 10, 100][[1]]

Crossrefs

Cf. A103712, A244921, A254140, A352453, A355183 (area).

Sequence in context: A243374 A309608 A324479 * A215479 A239725 A126583

Adjacent sequences: A355181 A355182 A355183 * A355185 A355186 A355187

Keyword

nonn,cons

Author

Amiram Eldar, Jun 23 2022

Status

approved