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A367496 Semiprimes k such that 2*k - 1 and 2*k + 1 are also semiprimes.

%I A367496 #15 Mar 28 2025 07:15:51
%S A367496 25,46,93,118,133,145,161,206,226,235,259,267,291,295,334,335,361,377,
%T A367496 395,407,447,497,529,573,579,583,669,674,685,694,695,781,843,898,899,
%U A367496 921,926,961,979,1059,1079,1114,1115,1142,1159,1214,1227,1241,1257,1285,1286,1294,1315,1379,1393,1405
%N A367496 Semiprimes k such that 2*k - 1 and 2*k + 1 are also semiprimes.
%C A367496 One of the three semiprimes k, 2*k - 1 and 2*k + 1 is 3 times a prime.
%H A367496 Robert Israel, <a href="/A367496/b367496.txt">Table of n, a(n) for n = 1..10000</a>
%e A367496 a(3) = 93 is a term because 93 = 3 * 31, 2 * 93 - 1 = 185 = 5 * 37 and 2 * 93 + 1 = 187 = 11 * 17 are semiprimes.
%p A367496 select(t -> numtheory:-bigomega(t) = 2 and numtheory:-bigomega(2*t-1) = 2 and numtheory:-bigomega(2*t+1) = 2, [$1..2000]);
%t A367496 Select[Range[1410],PrimeOmega[#]==PrimeOmega[2#+1]==PrimeOmega[2#-1]==2 &] (* _Stefano Spezia_, Nov 20 2023 *)
%Y A367496 Cf. A001358. Intersection of A111153 and A111168.
%K A367496 nonn
%O A367496 1,1
%A A367496 _Zak Seidov_ and _Robert Israel_, Nov 20 2023