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
Examples
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.
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.
Programs
-
Magma
[n: n in [0..600] | IsPrime(2*n-1) and IsPrime(8*n^2-14*n+7)]; // Vincenzo Librandi, Sep 22 2012
-
Mathematica
Select[ Range[1000], PrimeQ[2# - 1] && PrimeQ[8#^2 - 14# + 7] &] Select[Range[1000],AllTrue[{2#-1,8#^2-14#+7},PrimeQ]&] (* Harvey P. Dale, Apr 13 2025 *)
Comments