A108166 - OEIS

%I #26 Nov 26 2019 04:19:01

%S 25,55,85,115,121,145,187,205,235,253,265,289,295,319,355,391,415,445,

%T 451,493,505,517,529,535,565,583,649,655,667,685,697,745,781,799,835,

%U 841,865,895,901,913,943,955,979,985,1003,1081,1111,1135,1165,1177,1189

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

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

%C A108164 - the product of two primes of the form 6n + 1 (A002476),

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

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

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

%D 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.

%H Amiram Eldar, <a href="/A108166/b108166.txt">Table of n, a(n) for n = 1..10000</a>

%H Milton Abramowitz and Irene A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

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

%t Module[{nn = 150, pf}, pf = Select[6Range[nn] - 1, PrimeQ]; Take[Union[Times@@@Tuples[pf, 2]], nn/2]] (* _Harvey P. Dale_, Dec 09 2013 *)

%t Select[6Range[200] + 1, PrimeOmega[#] == 2 && Mod[FactorInteger[#][[1, 1]], 6] == 5 &] (* _Alonso del Arte_, Aug 24 2017 *)

%Y Cf. A001358, A007528.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Jun 13 2005

%E Edited and extended by _Ray Chandler_, Oct 15 2005