%I
%S 113,157,193,209,211,223,231,235,251,259,307,319,345,401,415,437,463,
%T 489,521,563,567,581,599,663,673,677,701,719,731,733,771,789,811,855,
%U 857,875,883,923,935,951,961,983,993,995,997,1017,1023,1031,1047,1089,1097
%N Numbers n such that 6*n+1, 3*n+2, 6*n+7 are all odd semiprimes.
%C Or odd numbers n such that the arithmetic progression 6*n+1, 6*n+4, 6*n+7 consists of twice a semiprime sandwiched between two semiprimes.
%t fQ[n_] := And[OddQ@ n, PrimeOmega@ n == 2]; Select[Range@ 1100,
%t AllTrue[{6 # + 1, 3 # + 2, 6 # + 7}, fQ] &] (* _Michael De Vlieger_, Nov 24 2015, Version 10 *)
%o (PARI) for(n=1, 1e4, if(n%2==1 && bigomega(6*n+1)==2 && bigomega(3*n+2)==2 && bigomega(6*n+7)==2, print1(n, ", "))); \\ _Altug Alkan_, Nov 24 2015
%Y Cf. A001358, A263510, A264779.
%K nonn
%O 1,1
%A _Vladimir Shevelev_ and _Peter J. C. Moses_, Nov 24 2015
