A200113 Decimal expansion of the area K of cyclic pentagon with sides 2, 3, 5, 7, and 11.

4, 1, 9, 5, 2, 9, 9, 2, 3, 6, 1, 3, 8, 0, 8, 9, 2, 4, 2, 5, 2, 7, 8, 6, 7, 3, 1, 3, 4, 4, 1, 3, 4, 9, 6, 9, 9, 5, 5, 6, 6, 2, 8, 1, 4, 2, 3, 8, 7, 4, 0, 0, 7, 5, 0, 7, 4, 1, 1, 5, 0, 0, 5, 6, 4, 7, 5, 0, 2, 4, 3, 0, 7, 4, 1, 5, 4, 5, 1, 8, 7, 5, 7, 3, 8, 3

Offset

2,1

Comments

s = {2,3,5,7,11}; R = circumradius (A200257).

K = sum((s(n)/4)(4*R^2-s(n)^2)^(1/2), n=1..5) = 41.9529923613808924252...

This is maximal area of pentagon with sides 2, 3, 5, 7, 11.

Links

Table of n, a(n) for n=2..87.

Mathematica

digits = 86; r = x /. FindRoot[ Sum[ ArcSin[ Prime[n]/2/x], {n, 5}] == Pi, {x, 5}, WorkingPrecision -> digits+10] // Re; Sum[p/4*(4*r^2 - p^2)^(1/2), {p, Prime /@ Range[5]}] // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 15 2013, after Zak Seidov *)

Crossrefs

Cf. A200257.

Sequence in context: A073364 A125165 A259448 * A065489 A346404 A332385

Adjacent sequences: A200110 A200111 A200112 * A200114 A200115 A200116

Keyword

nonn,cons

Author

Zak Seidov, Nov 18 2011

Status

approved