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A248347 Floor( 1/(Pi - 2^(n+1)*sin(Pi/2^(n+1)) ). 5
3, 12, 49, 198, 792, 3170, 12681, 50727, 202909, 811636, 3246545, 12986183, 51944732, 207778928, 831115713, 3324462855, 13297851421, 53191405684, 212765622737, 851062490950, 3404249963800, 13616999855201, 54467999420806, 217871997683226, 871487990732903 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.)

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..1000

FORMULA

a(n) ~ 6 * 4^(n+1) / Pi^3. - Vaclav Kotesovec, Oct 09 2014

EXAMPLE

n    Pi - Arch(n)      1/(Pi - Arch(n)

1    0.313166...         3.1932...

2    0.0801252...       12.4805...

3    0.0201475...       49.6339...

4    0.00504416...     198.249...

5    0.0012615...      792.709...

MATHEMATICA

z = 200; p[k_] := p[k] = (2^(k + 1))*Sin[Pi/2^(k + 1)]

Table[Floor[1/(Pi - p[n])], {n, 1, z}]  (* A248347  *)

CROSSREFS

Cf. A000027, A248355, A248357, A248355, A248360.

Sequence in context: A134589 A178872 A323263 * A037758 A037646 A012772

Adjacent sequences:  A248344 A248345 A248346 * A248348 A248349 A248350

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Oct 05 2014

STATUS

approved

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Last modified October 15 09:22 EDT 2019. Contains 328026 sequences. (Running on oeis4.)