A107890 Semiprimes that are the product of two members of A007645.

9, 21, 39, 49, 57, 91, 93, 111, 129, 133, 169, 183, 201, 217, 219, 237, 247, 259, 291, 301, 309, 327, 361, 381, 403, 417, 427, 453, 469, 471, 481, 489, 511, 543, 553, 559, 579, 589, 597, 633, 669, 679, 687, 703, 721, 723, 763, 793, 813, 817, 831, 849, 871

Offset: 1

Author

Jonathan Vos Post, Jun 12 2005

Keywords

• easy
• nonn

References

• Conway, J. H. and Guy, R. K., The Book of Numbers. New York: Springer-Verlag, pp. 220-223, 1996.
• Wagon, S. "Eisenstein Primes." Section 9.8 in Mathematica in Action. New York: W. H. Freeman, pp. 319-323, 1991.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Eisenstein Integer.
• Eric Weisstein's World of Mathematics, Eisenstein Prime.
• Eric Weisstein's World of Mathematics, Semiprime.

Crossrefs

Cf. A001358, A007645, A108164.

Programs

Maple

N:= 1000: # for terms <= N
P:= [3,op(select(isprime, [seq(i,i=1..N/3,6)]))]:
R:= NULL:
for i from 1 while P[i]^2 <= N do
  m:= ListTools:-BinaryPlace(P,N/P[i]+1/2);
  R:= R, seq(P[i]*P[j],j=i..m);
od:
sort([R]); # Robert Israel, Aug 28 2020

Formula

{a(n)} = {p*q: p and q both elements of A007645} = {p*q: p and q both of form 3*m^2 * n^2 for integers m, n}.

Extensions

Edited by Ray Chandler, Oct 15 2005

Definition corrected by N. J. A. Sloane, Feb 06 2008