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A102250
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Indices of semiprime Hauy rhombic dodecahedral numbers.
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2, 3, 4, 6, 12, 15, 16, 22, 34, 36, 51, 66, 87, 99, 100, 106, 117, 139, 141, 159, 166, 169, 174, 177, 180, 192, 201, 205, 232, 274, 282, 307, 337, 339, 342, 367, 370, 372, 379, 381, 411, 412, 429, 430, 432, 439, 444, 454, 460, 471, 477, 507, 510, 517, 555, 577
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Because the Hauy rhombic dodecahedral numbers A046142 are a(n) = (2*n-1)(8*n^2-14*n+7) no Hauy rhombic dodecahedral number can be prime.
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REFERENCES
| Hauy, R.-J. "Essai d'une theorie sur la structure des crystals appliquee a plusieurs genres de substances crystallisees." 1784.
Steinhaus, H. Mathematical Snapshots, 3rd ed. New York: Dover, pp. 185-186, 1999.
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LINKS
| Jonathan Vos Post, Table of Polytope Numbers, Sorted, Through 1,000,000 which lists Hauy rhombic dodecahedral numbers as "RhoDod(n)."
Eric Weisstein's World of Mathematics, Rhombic Dodecahedron.
Eric Weisstein's World of Mathematics, Hauy Construction.
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FORMULA
| Integers n such that both (2*n-1) and (8*n^2-14*n+7) are primes. Integers n such that (2*n-1)*(8*n^2-14*n+7) is an element in the intersection of A046142 and A001358.
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EXAMPLE
| a(3) = 4 because the 3rd Hauy rhombic dodecahedral number is A046142(3) = (2*4-1)(8*4^2-14*4+7) = 553 and because 553 = 7 * 79 is a semiprime.
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MATHEMATICA
| Select[ Range[1000], PrimeQ[2# - 1] && PrimeQ[8#^2 - 14# + 7] &]
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CROSSREFS
| Cf. A001358, A046142, A085601, A102130.
Sequence in context: A136291 A128393 A057919 * A084788 A002809 A173581
Adjacent sequences: A102247 A102248 A102249 * A102251 A102252 A102253
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 18 2005
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