A108164 Semiprimes p*q where both p and q are primes of the form 6n+1 (A002476).

49, 91, 133, 169, 217, 247, 259, 301, 361, 403, 427, 469, 481, 511, 553, 559, 589, 679, 703, 721, 763, 793, 817, 871, 889, 949, 961, 973, 1027, 1057, 1099, 1141, 1147, 1159, 1261, 1267, 1273, 1333, 1339, 1351, 1369, 1387, 1393, 1417, 1477, 1501, 1561, 1591

Offset: 1

Author

Jonathan Vos Post, Jun 13 2005

Keywords

• easy
• nonn

Comments

These are the products of terms from A107890 excluding multiples of 3.

Every semiprime not divisible by 2 or 3 must be in one of these three disjoint sets:

A108164 = the product of two primes of the form 6n+1 (A002476),

A108166 = the product of two primes of the form 6n-1 (A007528),

A108172 = the product of a prime of the form 6n+1 and a prime of the form 6n-1.

The product of two primes of the form 6n+1 is a semiprime of the form 6n+1.

References

• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 870.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
• K. G. Reuschle, Tafeln complexer Primzahlen, Königl. Akademie der Wissenschaften, Berlin, 1875, p. 1.

Crossrefs

Cf. A001358, A002476, A107890.

Programs

Maple

N:= 2000: # To get all terms <= N
P:= select(isprime, [seq(i,i=7..N/7, 6)]):
sort(select(`<=`,[seq(seq(P[i]*P[j],j=1..i),i=1..nops(P))],N)); # Robert Israel, Dec 27 2018

Mathematica

With[{nn=50},Take[Times@@@Tuples[Select[6*Range[nn]+1,PrimeQ],2]// Union,nn]] (* Harvey P. Dale, May 20 2021 *)

Formula

{a(n)} = {p*q where both p and q are in A002476}.

Extensions

Edited and extended by Ray Chandler, Oct 15 2005