A107982 - OEIS

%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