cp's OEIS Frontend

A108172 Semiprimes p*q where p is a prime of the form 6n+1 (A002476) and q is a prime of the form 6n-1 (A007528).

%I A108172 #20 May 08 2018 15:11:55
%S A108172 35,65,77,95,119,143,155,161,185,203,209,215,221,287,299,305,323,329,
%T A108172 335,341,365,371,377,395,407,413,437,473,485,497,515,527,533,545,551,
%U A108172 581,611,623,629,635,671,689,695,707,713,731,737,749,755,767,779,785
%N A108172 Semiprimes p*q where p is a prime of the form 6n+1 (A002476) and q is a prime of the form 6n-1 (A007528).
%C A108172 Also semiprimes of the form 6n-1 (or 6n+5).
%C A108172 Every semiprime not divisible by 2 or 3 must be in one of these three disjoint sets:
%C A108172 A108164 - the product of two primes of the form 6n+1 (A002476),
%C A108172 A108166 - the product of two primes of the form 6n-1 (A007528),
%C A108172 A108172 - the product of a prime of the form 6n+1 and a prime of the form 6n-1.
%C A108172 The product of a prime of the form 6n+1 and a prime of the form 6n-1 is a semiprime of the form 6n-1.
%C A108172 There are 740 of these numbers below 10,000.
%D A108172 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.
%H A108172 Vincenzo Librandi, <a href="/A108172/b108172.txt">Table of n, a(n) for n = 1..1000</a>
%H A108172 M. Abramowitz and I. 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 A108172 a(n) = 6 * A112776(n) + 5.
%t A108172 Select[Range[15,1000,2], Last/@FactorInteger[#]=={1,1} && IntegerQ[(#-2)/3]&] (* _Vladimir Joseph Stephan Orlovsky_, May 07 2011 *)
%o A108172 (PARI) list(lim)=my(v=List(),t); forprime(p=5, lim\7, if(p%6<5, next); forprime(q=7, lim\5, if(q%6>1, next); t=p*q; if(t>lim, break); listput(v, t))); Set(v) \\ _Charles R Greathouse IV_, Feb 08 2017
%Y A108172 Cf. A001358, A002476, A007528, A190299.
%K A108172 easy,nonn
%O A108172 1,1
%A A108172 _Jonathan Vos Post_, Jun 13 2005
%E A108172 Edited by _Ray Chandler_, Oct 15 2005