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A108164
Semiprimes p*q where both p and q are primes of the form 6n+1 (A002476).
6
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
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
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Jun 13 2005
EXTENSIONS
Edited and extended by Ray Chandler, Oct 15 2005
STATUS
approved