

A119659


Floor of the area of consecutive PrimeIndexed Prime triangles.


0



240, 599, 1197, 1957, 2777, 4475, 6870, 9727, 13111, 16006, 19318, 24588, 30446, 37372, 43923, 52863, 59912, 68278, 79653, 93050, 109121, 125459, 138200, 146888, 156205, 175051, 201823, 236438, 255780, 282105, 307211, 338310, 365530, 397086
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OFFSET

1,1


COMMENTS

Conjecture: The triples (3,5,11), (5,11,17), (11,17,31) are the only consecutive PIP triples that cannot form a triangle.


LINKS



FORMULA

A prime index is the numerical position of a prime number in the sequence of prime numbers. A PrimeIndexed Prime (PIP) is a prime number whose index is also prime. A PrimeIndexed Prime triangle is a triangle whose sides are PrimeIndexed Primes.


EXAMPLE

The first set of consecutive PIPs that produces a triangle, 17, 31 and 41, produces the 17 X 31 X 41 unit triangle whose area is 240.462... square units.


MATHEMATICA

ar[n_]:=Module[{a=First[n], b=n[[2]], c=Last[n], s}, s=Total[{a, b, c}]/2; Sqrt[s(sa)(sb)(sc)]]; Floor[ar[#]]&/@Partition[Select[Prime[ Range[6, 200]], PrimeQ[PrimePi[#]]&], 3, 1] (* Harvey P. Dale, Jun 29 2011 *)


PROG

(PARI) area(n) = for(x=1, n, a=prime(prime(x)); b=prime(prime(x+1)); c=prime(prime(x+2)); if(a+b<=c, p=a+b+c; y =1/4*sqrt(p*(p2*a)*(p2*b)*(p2*c)); print1(floor(y)", ")))


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



