A255405 a(n) = floor((2/sqrt(Pi))^n).

1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 6, 6, 7, 8, 9, 11, 12, 14, 16, 18, 20, 23, 26, 29, 33, 37, 42, 47, 53, 60, 68, 77, 87, 98, 111, 125, 141, 159, 180, 203, 229, 258, 292, 329, 371, 419, 473, 534, 602, 680, 767, 865, 977, 1102, 1244, 1403, 1584, 1787, 2016, 2275, 2567

Offset: 0

Author

Kival Ngaokrajang, Feb 22 2015

Keywords

• nonn

Comments

Inspired by squaring the circle and Vitruvian Man, but starting with a unit circle and a square whose sides are of length sqrt(Pi), A002161. a(n) is the curvature (rounded down) of the n-th circle. See illustrations in the links.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Kival Ngaokrajang, Illustration of initial terms.
• Wikipedia, Squaring the circle.

Crossrefs

Cf. A002161, A255162, A255163.

Programs

Mathematica

Table[Floor[(2/Sqrt[Pi])^n], {n,0,50}] (* G. C. Greubel, Jan 09 2017 *)

PARI

{for(n=1,100,a=floor(2^n/sqrt(Pi)^n);print1(a,", "))}

Formula

a(n) = floor((2/sqrt(Pi))^n).