A121388 -id:A121388 - cp's OEIS frontend

A107978 Products of two primes of the form 4n+3 (A002145).

9, 21, 33, 49, 57, 69, 77, 93, 121, 129, 133, 141, 161, 177, 201, 209, 213, 217, 237, 249, 253, 301, 309, 321, 329, 341, 361, 381, 393, 413, 417, 437, 453, 469, 473, 489, 497, 501, 517, 529, 537, 553, 573, 581, 589, 597, 633, 649, 669, 681, 713, 717, 721, 737

Offset: 1

Jonathan Vos Post, Jun 12 2005

Every odd semiprime must be in one of three disjoint sets: the product of two primes of the form 4n+1 (A121387), the product of two primes of the form 4n+3 (A107978), or the product of a prime of the form 4n+1 and a prime of the form 4n+3 (A080774).

T. D. Noe, Table of n, a(n) for n=1..1000
Eric Weisstein's World of Mathematics, Semiprime.

Cf. A001358, A002145, A080774, A121387.
Union of A131574 and A080109.
Third row of A121388.

p = Select[ Prime@ Range@ 60, Mod[ #, 4] == 3 &]; Take[ Sort@ Flatten@ Table[ p[[i]] p[[j]], {j, 30}, {i, j}], 54] (* or *)
fQ[n_] := Block[{fi = FactorInteger@ n}, Plus @@ Last /@ fi == 2 && Union@ Mod[ First /@ fi, 4] == {3}]; Select[ Range@ 748, fQ@# &] (* Robert G. Wilson v, May 20 2010 *)

{a(n)} = {p*q: p and q both elements of A002145}.

Edited by N. J. A. Sloane, May 20 2010

A121387 Semiprimes p*q with p and q primes of the form 4k+1 (A002144).

Original entry on oeis.org

25, 65, 85, 145, 169, 185, 205, 221, 265, 289, 305, 365, 377, 445, 481, 485, 493, 505, 533, 545, 565, 629, 685, 689, 697, 745, 785, 793, 841, 865, 901, 905, 949, 965, 985, 1037, 1073, 1145, 1157, 1165, 1189, 1205, 1241, 1261, 1285, 1313, 1345, 1369, 1385, 1405, 1417

Offset: 1

Alford Arnold, Jul 26 2006, corrected Jun 24 2007

p and q can be the same. [Harvey P. Dale, Jan 15 2012]

The terms are semiprimes of the form 4k + 1, and comprise only a portion of all such semiprimes, see A108181. - Richard R. Forberg, Aug 27 2013

			65 = 5 * 13. Note that 5 mod 4 = 1 and 13 mod 4 = 1, so 65 is a term.

François Huppé, Table of n, a(n) for n = 1..10000 (First 1000 terms from T. D. Noe).

Cf. A001358, A002144.
Fifth row of A121388.
Union of A080109 and A131574.
Cf. A107978, A080774, A108181.

With[{prs=Select[Prime[Range[150]],Mod[#,4]==1&]},Take[Union[Times @@@ Tuples[prs,2]],60]] (* Harvey P. Dale, Jan 15 2012 *)

Better definition from T. D. Noe, Sep 25 2007

cp's OEIS Frontend

A107978 Products of two primes of the form 4n+3 (A002145).

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