This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A248347 #21 Nov 11 2024 21:19:38
%S A248347 3,12,49,198,792,3170,12681,50727,202909,811636,3246545,12986183,
%T A248347 51944732,207778928,831115713,3324462855,13297851421,53191405684,
%U A248347 212765622737,851062490950,3404249963800,13616999855201,54467999420806,217871997683226,871487990732903
%N A248347 a(n) = floor(1/(Pi - 2^(n+1)*sin(Pi/2^(n+1)))).
%C A248347 Let Arch(n) = 2^(n+1)*sin(Pi/2^(n+1)) be the Archimedean approximation to Pi (Finch, pp. 17 and 23) given by a regular polygon of 2^(n+1) sides. A248347 provides insight into the manner of convergence of Arch(n) to Pi. Another provider is the fact that the least k for which Arch(k) < 1/4^n is A000027(n) = n. (For the closely related function arch, see A248355.)
%H A248347 Clark Kimberling, <a href="/A248347/b248347.txt">Table of n, a(n) for n = 1..1000</a>
%F A248347 a(n) ~ 6 * 4^(n+1) / Pi^3. - _Vaclav Kotesovec_, Oct 09 2014
%e A248347 n Pi - Arch(n) 1/(Pi - Arch(n))
%e A248347 1 0.313166... 3.1932...
%e A248347 2 0.0801252... 12.4805...
%e A248347 3 0.0201475... 49.6339...
%e A248347 4 0.00504416... 198.249...
%e A248347 5 0.0012615... 792.709...
%t A248347 z = 200; p[k_] := p[k] = (2^(k + 1))*Sin[Pi/2^(k + 1)]
%t A248347 Table[Floor[1/(Pi - p[n])], {n, 1, z}] (* A248347 *)
%Y A248347 Cf. A000027, A248355, A248357, A248355, A248360.
%K A248347 nonn,easy
%O A248347 1,1
%A A248347 _Clark Kimberling_, Oct 05 2014