

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
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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[(ca)^2+(db)^2], y=Sqrt[(df)^2+(ce)^2], z=Sqrt[(ea)^2+(fb)^2], s}, s=(x+y+z)/2; Sqrt[s(sx)(sy)(sz)]]; 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



