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Search: id:A104012
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| 1, 2, 3, 5, 6, 11, 14, 15, 21, 26, 30, 35, 36, 44, 54, 63, 69, 74, 81, 114, 128, 131, 135, 138, 153, 165, 168, 191, 194
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OFFSET
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1,2
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COMMENT
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Because the cubic polynomial for centered dodecahedral numbers factors into n time an irreducible quadratic, the dodecahedral numbers can never be prime, but can be semiprime iff (2*n+1) is prime and (5*n^2+5*n+1) is prime. Centered dodecahedral numbers (A005904) are not to be confused with dodecahedral numbers (A006566) = n(3n-1)(3n-2)/2, nor with rhombic dodecahedral numbers (A005917).
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REFERENCES
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B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.
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FORMULA
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n such that A001222(A005904(n)) = 2. n such that Bigomega((2*n+1)*(5*n^2 + 5*n + 1)). n such that A104011(n) = 2.
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EXAMPLE
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a(1) = 1 because A005904(1) = 33 = 3 * 11, which is semiprime.
a(2) = 2 because A005904(2) = 155 = 5 * 31, which is semiprime.
a(3) = 3 because A005904(3) = 427 = 7 * 61, which is semiprime.
a(4) = 5 because A005904(5) = 1661 = 11 * 151.
194 is in this sequence because A005904(194) = 73579739 = 389 * 189151, which is semiprime.
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CROSSREFS
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Cf. A001222, A001358, A005904, A104011.
Adjacent sequences: A104009 A104010 A104011 this_sequence A104013 A104014 A104015
Sequence in context: A137808 A091909 A100883 this_sequence A039037 A050049 A132581
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 24 2005
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