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A154924 Area of prime triangles. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A330251 A175645 A178514 * A071105 A218113 A295194

Adjacent sequences:  A154921 A154922 A154923 * A154925 A154926 A154927

KEYWORD

easy,nonn

AUTHOR

Gil Broussard, Jan 17 2009

STATUS

approved

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Last modified April 20 19:33 EDT 2021. Contains 343137 sequences. (Running on oeis4.)