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A108166 Semiprimes p*q where both p and q are primes of the form 6n-1 (A007528). 8
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A206075 A276448 A176275 * A080863 A339729 A091214
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Jun 13 2005
EXTENSIONS
Edited and extended by Ray Chandler, Oct 15 2005
STATUS
approved

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)