A108166 Semiprimes p*q where both p and q are primes of the form 6n-1 (A007528).

25, 55, 85, 115, 121, 145, 187, 205, 235, 253, 265, 289, 295, 319, 355, 391, 415, 445, 451, 493, 505, 517, 529, 535, 565, 583, 649, 655, 667, 685, 697, 745, 781, 799, 835, 841, 865, 895, 901, 913, 943, 955, 979, 985, 1003, 1081, 1111, 1135, 1165, 1177, 1189

Offset

1,1

Comments

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

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

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Formula

{a(n)} = {p*q where both p and q are in A007528}.

Mathematica

Module[{nn = 150, pf}, pf = Select[6Range[nn] - 1, PrimeQ]; Take[Union[Times@@@Tuples[pf, 2]], nn/2]] (* Harvey P. Dale, Dec 09 2013 *)
Select[6Range[200] + 1, PrimeOmega[#] == 2 && Mod[FactorInteger[#][[1, 1]], 6] == 5 &] (* Alonso del Arte, Aug 24 2017 *)

Crossrefs

Cf. A001358, A007528.

Sequence in context: A206075 A276448 A176275 * A080863 A339729 A091214

Adjacent sequences: A108163 A108164 A108165 * A108167 A108168 A108169

Keyword

easy,nonn

Author

Jonathan Vos Post, Jun 13 2005

Extensions

Edited and extended by Ray Chandler, Oct 15 2005

Status

approved