A154924 Area of prime triangles.

3, 6, 0, 0, 12, 6, 16, 18, 16, 6, 32, 6, 36, 8, 28, 16, 2, 26, 10, 6, 10, 54, 6, 18, 0, 36, 0, 132, 18, 68, 12, 40, 24, 12, 20, 22, 20, 12, 24, 48, 0, 66, 30, 120, 150, 24, 62, 6, 4, 32, 48, 24, 8, 0, 28, 16, 18, 84, 90, 180, 18, 144, 6, 132, 52, 36, 44, 54, 28, 38, 14

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

Take six consecutive primes and group them in ordered pairs (p1,p2) (p3,p4) (p5,p6) and compute the area of the triangle they form in the Cartesian plane.

Example

a(1)=3 because the triangle with vertices (2,3)(5,7)(11,13) has an area of 3. a(2)=6 because the triangle with vertices (3,5)(7,11)(13,17) has an area of 6. a(3)=0 because the vertices (5,7)(11,13)(17,19) are collinear and do not form a triangle.

Mathematica

artr[{a_, b_, c_, d_, e_, f_}]:=Module[{x=Sqrt[(c-a)^2+(d-b)^2], y=Sqrt[(d-f)^2+(c-e)^2], z=Sqrt[(e-a)^2+(f-b)^2], s}, s=(x+y+z)/2; Sqrt[s(s-x)(s-y)(s-z)]]; artr/@Partition[Prime[Range[80]], 6, 1]//Simplify (* Harvey P. Dale, Dec 30 2020 *)

Crossrefs

Sequence in context: A175645 A178514 A371334 * A071105 A218113 A295194

Adjacent sequences: A154921 A154922 A154923 * A154925 A154926 A154927

Keyword

easy,nonn

Author

Gil Broussard, Jan 17 2009

Status

approved