This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A102250 #28 Apr 13 2025 14:35:29
%S A102250 2,3,4,6,12,15,16,22,34,36,51,66,87,99,100,106,117,139,141,159,166,
%T A102250 169,174,177,180,192,201,205,232,274,282,307,337,339,342,367,370,372,
%U A102250 379,381,411,412,429,430,432,439,444,454,460,471,477,507,510,517,555,577
%N A102250 Indices of semiprime Haüy rhombic dodecahedral numbers.
%C A102250 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.
%C A102250 Integers n such that both (2*n-1) and (8*n^2-14*n+7) are primes.
%C A102250 Integers n such that (2*n-1)*(8*n^2-14*n+7) is an element in the intersection of A046142 and A001358.
%D A102250 R.-J. Haüy, Essai d'une théorie sur la structure des crystaux appliquée à plusieurs genres de substances crystallisées, 1784.
%D A102250 H. Steinhaus, Mathematical Snapshots, 3rd ed. New York: Dover, pp. 185-186, 1999.
%H A102250 Vincenzo Librandi, <a href="/A102250/b102250.txt">Table of n, a(n) for n = 1..1000</a>
%H A102250 Jonathan Vos Post, <a href="http://magicdragon.com/poly.html">Table of Polytope Numbers, Sorted, Through 1,000,000</a> which lists Haüy rhombic dodecahedral numbers as "RhoDod(n).
%H A102250 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RhombicDodecahedron.html">Rhombic Dodecahedron</a>.
%H A102250 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HauyConstruction.html">Haüy Construction.</a>
%e A102250 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.
%t A102250 Select[ Range[1000], PrimeQ[2# - 1] && PrimeQ[8#^2 - 14# + 7] &]
%t A102250 Select[Range[1000],AllTrue[{2#-1,8#^2-14#+7},PrimeQ]&] (* _Harvey P. Dale_, Apr 13 2025 *)
%o A102250 (Magma) [n: n in [0..600] | IsPrime(2*n-1) and IsPrime(8*n^2-14*n+7)]; // _Vincenzo Librandi_, Sep 22 2012
%Y A102250 Cf. A001358, A046142, A085601, A102130.
%K A102250 easy,nonn
%O A102250 1,1
%A A102250 _Jonathan Vos Post_, Feb 18 2005