A119659 Floor of the area of consecutive Prime-Indexed Prime triangles.

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

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

Table of n, a(n) for n=1..34.

Formula

A prime index is the numerical position of a prime number in the sequence of prime numbers. A Prime-Indexed Prime (PIP) is a prime number whose index is also prime. A Prime-Indexed Prime triangle is a triangle whose sides are Prime-Indexed 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(s-a)(s-b)(s-c)]]; 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*(p-2*a)*(p-2*b)*(p-2*c)); print1(floor(y)", ")))

Crossrefs

Sequence in context: A300145 A063372 A070123 * A263161 A268772 A202196

Adjacent sequences: A119656 A119657 A119658 * A119660 A119661 A119662

Keyword

nonn

Author

Cino Hilliard, Jul 28 2006

Status

approved