%I #8 Apr 16 2023 20:34:04
%S 11733,15117,17245,28113,32365,34413,48745,78481,93453,101665,102957,
%T 105333,108753,134097,143101,157713,163801,170853,190621,208293,
%U 212545,233097,273417,274893,294301,300385,323281,346497,354565,363777,390205,405357,470341,500217,501477,542193,555153,561205
%N Semiprimes k such that k+1, k+2, 2*k+1 and 2*k+3 are also semiprimes.
%C Numbers k such that 2*k+1 and 2*k+3 are both in A092192.
%C All terms == 1 or 33 (mod 36).
%H Robert Israel, <a href="/A362200/b362200.txt">Table of n, a(n) for n = 1..1000</a>
%e a(3) = 17245 is a term because 17245 = 5 * 3449, 17246 = 2 * 8623, 17247 = 3 * 5749, 2 * 17245 + 1 = 34491 = 3 * 11497 and 2 * 17245 + 3 = 34493 = 17 * 2029 are all semiprimes.
%p SP:= select(t -> numtheory:-bigomega(t)=2, {$1..2*10^6}):
%p A:= SP intersect map(`-`,SP,1) intersect map(`-`,SP,2):
%p SPO:= select(type,SP,odd):
%p A:= A intersect map(t -> (t-1)/2, SPO) intersect map(t -> (t-3)/2, SPO):
%p sort(convert(A,list));
%Y Cf. A001358, A092192.
%K nonn
%O 1,1
%A _Zak Seidov_ and _Robert Israel_, Apr 10 2023