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A119659
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Floor of the area of consecutive Prime-Index-Prime triangles.
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0
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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; internal format)
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OFFSET
| 1,1
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COMMENTS
| Conjecture: The triples (3,5,11),(5,11,17),(11,17,31) are the only consecutive PIP triples that cannot form a triangle.
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FORMULA
| A prime index is the numerical position of a prime number in the sequence of prime numbers. A Prime-Index-Prime (PIP) is a prime number whose index is also prime. A Prime-Index-Prime triangle is a triangle whose sides are Prime-Index- Primes.
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EXAMPLE
| The first set of consecutive PIPs that produces a triangle, 17,31 and 41,
produces the 17x31x41 unit triangle whose area is 240.462.. square units.
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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] (* From Harvey P. Dale, June 29 2011 *)
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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)", ")))
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CROSSREFS
| Sequence in context: A154378 A063372 A070123 * A202196 A060663 A092000
Adjacent sequences: A119656 A119657 A119658 * A119660 A119661 A119662
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KEYWORD
| nonn
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AUTHOR
| Cino Hilliard (hillcino368(AT)gmail.com), Jul 28 2006
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