%I #8 Feb 16 2021 02:08:00
%S 145,203,291,298,407,497,649,707,758,815,899,926,959,995,1079,1094,
%T 1139,1142,1157,1313,1403,1415,1461,1497,1538,1639,1658,1691,1857,
%U 1934,1945,1991,2123,2159,2217,2234,2315,2603,2629,2807,2991,3215,3254,3279,3305
%N Numbers k that are the products of two distinct primes such that 2*k+1, 4*k+3 and 8*k+7 are also products of two distinct primes.
%e 145 is a term because 145 = 5*29, 2*145 + 1 = 291 = 3*97, 4*145 + 1 = 583 = 11*53, and 8*145 + 1 = 1167 = 3*389.
%t f[n_]:=Last/@FactorInteger[n]=={1,1}; lst={};Do[If[f[n]&&f[2*n+1]&&f[4*n+3]&&f[8*n+7],AppendTo[lst,n]],{n,0,2*7!}];lst
%Y Cf. A006881, A111153, A177210, A177211, A177212, A177213, A177214, A177215, A177216, A177217, A177220, A177221, A177222.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, May 05 2010