A107982 Gaussian-Pythagorean semiprimes. Products of a prime of the form 2 or 4n+1 (A002313) and a prime of the form 4n+3 (A002145).

6, 14, 15, 22, 35, 38, 39, 46, 51, 55, 62, 86, 87, 91, 94, 95, 111, 115, 118, 119, 123, 134, 142, 143, 155, 158, 159, 166, 183, 187, 203, 206, 214, 215, 219, 235, 247, 254, 259, 262, 267, 278, 287, 291, 295, 299, 302, 303, 319, 323, 326, 327, 334, 335, 339, 355

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..56.

Eric Weisstein's World of Mathematics, Semiprime.

Formula

{a(n)} = {p*q: p in A002313 and q in A002145}.

Mathematica

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 *)

Crossrefs

Cf. A001358, A002313, A002145.

Sequence in context: A230873 A192321 A190272 * A341448 A081535 A355941

Adjacent sequences: A107979 A107980 A107981 * A107983 A107984 A107985

Keyword

easy,nonn

Author

Jonathan Vos Post, Jun 12 2005

Status

approved