A102250 Indices of semiprime Haüy rhombic dodecahedral numbers.

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

Offset

1,1

Comments

Because the Haüy rhombic dodecahedral numbers are A046142(n) = (2*n-1)(8*n^2-14*n+7) no Haüy rhombic dodecahedral number can be prime.

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.

References

R.-J. Haüy, Essai d'une théorie sur la structure des crystaux appliquée à plusieurs genres de substances crystallisées, 1784.

H. Steinhaus, Mathematical Snapshots, 3rd ed. New York: Dover, pp. 185-186, 1999.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Jonathan Vos Post, Table of Polytope Numbers, Sorted, Through 1,000,000 which lists Haüy rhombic dodecahedral numbers as "RhoDod(n).

Eric Weisstein's World of Mathematics, Rhombic Dodecahedron.

Eric Weisstein's World of Mathematics, Haüy Construction.

Example

a(3) = 4 because the 3rd Haüy rhombic dodecahedral number is A046142(3) = (2*4-1)(8*4^2-14*4+7) = 553 and because 553 = 7 * 79 is a semiprime.

Mathematica

Select[ Range[1000], PrimeQ[2# - 1] && PrimeQ[8#^2 - 14# + 7] &]

Prog

(Magma) [n: n in [0..600] | IsPrime(2*n-1) and IsPrime(8*n^2-14*n+7)]; // Vincenzo Librandi, Sep 22 2012

Crossrefs

Cf. A001358, A046142, A085601, A102130.

Sequence in context: A128393 A368988 A057919 * A084788 A002809 A015904

Adjacent sequences: A102247 A102248 A102249 * A102251 A102252 A102253

Keyword

easy,nonn

Author

Jonathan Vos Post, Feb 18 2005

Status

approved