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A264043 Numbers n such that n and n+3 are consecutive semiprimes.

%I A264043 #10 Feb 08 2016 20:32:53
%S A264043 6,22,35,46,62,74,82,115,155,166,206,259,262,295,323,355,358,362,395,
%T A264043 466,478,482,502,511,559,562,583,586,611,623,626,671,703,718,731,734,
%U A264043 746,755,763,799,835,838,862,866,886,895,914,923,955,979,982
%N A264043 Numbers n such that n and n+3 are consecutive semiprimes.
%H A264043 Charles R Greathouse IV, <a href="/A264043/b264043.txt">Table of n, a(n) for n = 1..10000</a>
%F A264043 a(n) >> n log n. - _Charles R Greathouse IV_, Nov 02 2015
%e A264043 6 and 9 are 2nd and 3rd semiprimes, or 6=A001358(2) and 9=A001358(3);
%e A264043 22=A001358(8) and 25=A001358(9).
%t A264043 Flatten[Position[Partition[Table[If[PrimeOmega[n]==2,1,0],{n,1000}], 4,1],_?(#=={1,0,0,1}&)]] (* _Harvey P. Dale_, Feb 08 2016 *)
%o A264043 (PARI) for(n=1, 1e3, if(bigomega(n) == 2 && bigomega(n+3) == 2 && bigomega(n+1) !=2 && bigomega(n+2) !=2, print1(n", "))) \\ _Altug Alkan_, Nov 02 2015
%o A264043 (PARI) is(n)=if(n%4==2, isprime(n/2) && bigomega(n+3)==2 && bigomega(n+1)!=2, n%4==3 && isprime((n+3)/2) && bigomega(n)==2 && bigomega(n+2)!=2) \\ _Charles R Greathouse IV_, Nov 02 2015
%Y A264043 Cf. A001358, A065516, A136196.
%K A264043 nonn
%O A264043 1,1
%A A264043 _Zak Seidov_, Nov 02 2015