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%I #8 Nov 21 2013 12:48:42
%S 6,14,15,22,35,38,39,46,51,55,62,86,87,91,94,95,111,115,118,119,123,
%T 134,142,143,155,158,159,166,183,187,203,206,214,215,219,235,247,254,
%U 259,262,267,278,287,291,295,299,302,303,319,323,326,327,334,335,339,355
%N Gaussian-Pythagorean semiprimes. Products of a prime of the form 2 or 4n+1 (A002313) and a prime of the form 4n+3 (A002145).
%C Every semiprime must be in one of these three disjoint sets: the product of two primes of the form x^2+y^2, the product of two primes of the form x^2+3y^2, or the product of a prime of the form x^2+y^2 and a prime of the form x^2+3y^2. Equivalently, every semiprime must be in one of these three disjoint sets: the product of two primes of the form x^2+y^2 (2 or 4n+1), or the product of two primes of the form 4n+3, or the product of a prime of the form x^2+y^2 and a prime of the form 4n+3. In the latter case, such a semiprime is itself either of the form 4n+3 or the form 8n+6.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Semiprime.html">Semiprime.</a>
%F {a(n)} = {p*q: p in A002313 and q in A002145}.
%t Module[{nn=60,f1,f2,minlen},f1=Join[{2},Select[4Range[0,nn]+1,PrimeQ]];f2=Select[4Range[0,nn]+3,PrimeQ];minlen=Min[Length[f1],Length[f2]];Take[Union[Flatten[Outer[Times,Take[f1,minlen],Take[f2,minlen]]]],nn]] (* _Harvey P. Dale_, May 06 2012 *)
%Y Cf. A001358, A002313, A002145.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Jun 12 2005
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