login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A248358 Floor(1/(Pi - n*sin(Pi/n))). 5
0, 0, 1, 3, 4, 7, 9, 12, 15, 19, 23, 27, 32, 38, 43, 49, 56, 62, 69, 77, 85, 93, 102, 111, 121, 130, 141, 151, 162, 174, 186, 198, 210, 223, 237, 250, 265, 279, 294, 309, 325, 341, 357, 374, 391, 409, 427, 445, 464, 483, 503, 523, 543, 564, 585, 606, 628 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

For n > 1, let arch(n) = n*sin(Pi/n) be the Archimedean approximation to Pi (Finch, pp. 17 and 23) given by a regular polygon of n+1 sides.  A248358 and A248355 provide insight into the manner of convergence of arch(n) to Pi.  (For the closely related function Arch, see A248347.)

See A248578 for the similar sequence round(1/(Pi-n*sin(Pi/n))). - M. F. Hasler, Oct 08 2014

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000

FORMULA

a(n) ~ 6*n^2/Pi^3. - Vaclav Kotesovec, Oct 09 2014

EXAMPLE

n    Pi - arch(n)    1/(Pi - arch(n))

1     3.14159...       0.3183...

2     1.14159...       0.8759...

3     0.54351...       1.8398...

4     0.31316...       3.1932...

5     0.20266...       4.9342...

6     0.14159...       7.0625...

MATHEMATICA

z = 200; p[k_] := p[k] = k*Sin[Pi/k]; N[Table[Pi - p[n], {n, 1, z/10}]]

f[n_] := f[n] = Select[Range[z], Pi - p[#] < 1/(2 n) &, 1]

u = Flatten[Table[f[n], {n, 1, z}]]        (* A248355 *)

v = Flatten[Position[Differences[u], 0]]   (* A248356 *)

w = Flatten[Position[Differences[u], 1]]   (* A248357 *)

f = Table[Floor[1/(Pi - p[n])], {n, 1, z}] (* A248358 *)

PROG

(PARI) a(n)=1\(Pi-n*sin(Pi/n)) \\ M. F. Hasler, Oct 08 2014

CROSSREFS

Cf. A248355, A248356, A248357, A248347, A248578.

Sequence in context: A246514 A060142 A049844 * A244952 A140402 A005539

Adjacent sequences:  A248355 A248356 A248357 * A248359 A248360 A248361

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Oct 05 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 26 17:36 EST 2021. Contains 340442 sequences. (Running on oeis4.)