%I #10 May 07 2024 07:02:40

%S 11,24,31,44,69,71,92,99,100,101,107,108,109,123,125,128,131,132,148,

%T 160,181,184,204,207,224,235,243,245,249,251,263,267,271,288,289,297,

%U 304,332,347,348,355,357,359,360,364,371,373,380,384,389,400,420,423,445,448,449,451,459,460,465,485

%N Numbers k such that 2*k + 3 and 3*k + 2 are semiprimes.

%C The first k where k, k + 1 and k + 2 are all terms is 99. There is no k where k, k + 1, k + 2 and k + 3 are all terms, because 3 * t + 2 is divisible by 4 for t = one of these.

%H Robert Israel, <a href="/A372582/b372582.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 31 is a term because 2 * 31 + 3 = 65 = 5 * 13 and 3 * 31 + 2 = 95 = 5 * 19 are both semiprimes.

%p filter:= k -> numtheory:-bigomega(3*k+2) = 2 and numtheory:-bigomega(2*k+3) = 2:

%p select(filter, [$1..1000]);

%t s = {}; Do[If[2 == PrimeOmega[2*k + 3] == PrimeOmega[3*k + 2], AppendTo[s, k]], {k, 10^3}]; s

%Y Cf. A001358.

%K nonn,new

%O 1,1

%A _Zak Seidov_ and _Robert Israel_, May 05 2024