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

1,1

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.

Formula

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

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 *)

Crossrefs

Cf. A001358, A002476, A107890.

Sequence in context: A118886 A198773 A320633 * A020158 A084632 A020176

Adjacent sequences: A108161 A108162 A108163 * A108165 A108166 A108167

Keyword

easy,nonn

Author

Jonathan Vos Post, Jun 13 2005

Extensions

Edited and extended by Ray Chandler, Oct 15 2005

Status

approved