A255405 - OEIS

%I #20 May 23 2024 06:30:05

%S 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,

%T 37,42,47,53,60,68,77,87,98,111,125,141,159,180,203,229,258,292,329,

%U 371,419,473,534,602,680,767,865,977,1102,1244,1403,1584,1787,2016,2275,2567

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

%C 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.

%H G. C. Greubel, <a href="/A255405/b255405.txt">Table of n, a(n) for n = 0..5000</a>

%H Kival Ngaokrajang, <a href="/A255405/a255405.pdf">Illustration of initial terms</a>.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Squaring_the_circle">Squaring the circle</a>.

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

%t Table[Floor[(2/Sqrt[Pi])^n], {n,0,50}] (* _G. C. Greubel_, Jan 09 2017 *)

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

%Y Cf. A002161, A255162, A255163.

%K nonn

%O 0,6

%A _Kival Ngaokrajang_, Feb 22 2015