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A119659 Floor of the area of consecutive Prime-Indexed 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 23 12:26 EST 2022. Contains 350511 sequences. (Running on oeis4.)