OFFSET
0,1
COMMENTS
The average difference between terms in the sequence approaches 2*Pi.
Limit_{n -> oo} d/dn (Pi / arcsin(1/2n)) = 2*Pi.
FORMULA
a(n) = ceiling( Pi / arcsin(1/(2*n)) ).
EXAMPLE
a(0) = 3, since this is the smallest number of sides a regular polygon may have;
a(1) = ceiling( Pi / arcsin(1/2) ) = ceiling( Pi/(Pi/6) ) = 6;
a(2) = ceiling( Pi / arcsin(1/4) ) = ceiling( Pi/(0.2526...) ) = 13;
...
MATHEMATICA
Table[If[n == 0, 3, Ceiling[Pi/ArcSin[1/(2 n)]]], {n, 0, 50}] (* Michael De Vlieger, Oct 28 2016 *) (* corrected on Aug 28 2023 by John D. Dixon *)
PROG
(PARI) a(n) = if (n==0, 3, ceil(Pi/asin(1/(2*n)))); \\ Michel Marcus, Oct 28 2016; corrected Jun 13 2022 \\ corrected again on Aug 28 2023 by John D. Dixon
CROSSREFS
KEYWORD
nonn
AUTHOR
John D. Dixon, Oct 26 2016
EXTENSIONS
First term and definition corrected by John D. Dixon, Aug 28 2023
STATUS
approved