|
| |
|
|
A104012
|
|
Indices of centered dodecahedral numbers (A005904) which are semiprimes (A001358).
|
|
1
| |
|
|
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
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| 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).
|
|
|
REFERENCES
| B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.
|
|
|
FORMULA
| 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.
|
|
|
EXAMPLE
| 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.
|
|
|
CROSSREFS
| Cf. A001222, A001358, A005904, A104011.
Sequence in context: A091909 A171040 A100883 * A164830 A039037 A050049
Adjacent sequences: A104009 A104010 A104011 * A104013 A104014 A104015
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 24 2005
|
| |
|
|
