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Search: id:A119659
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| A119659 |
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Floor of the area of consecutive Prime-Index-Prime triangles. |
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+0
1
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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; listen)
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OFFSET
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1,1
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COMMENT
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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
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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
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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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PROGRAM
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(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
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Sequence in context: A099833 A063372 A070123 this_sequence A060663 A092000 A124352
Adjacent sequences: A119656 A119657 A119658 this_sequence A119660 A119661 A119662
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KEYWORD
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nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Jul 28 2006
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