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A277690
Smallest possible number of sides of a regular polygon with unit sides and circumradius at least n.
1
3, 6, 13, 19, 26, 32, 38, 44, 51, 57, 63, 70, 76, 82, 88, 95, 101, 107, 114, 120, 126, 132, 139, 145, 151, 158, 164, 170, 176, 183, 189, 195, 202, 208, 214, 220, 227, 233, 239, 246, 252, 258, 264, 271, 277, 283, 290, 296, 302, 308, 315
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
See A004082 for another version.
As a function, this is the inverse of A067099.
Sequence in context: A078382 A075651 A091277 * A136484 A263621 A137039
KEYWORD
nonn
AUTHOR
John D. Dixon, Oct 26 2016
EXTENSIONS
First term and definition corrected by John D. Dixon, Aug 28 2023
STATUS
approved