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%I A372582 #10 May 07 2024 07:02:40
%S A372582 11,24,31,44,69,71,92,99,100,101,107,108,109,123,125,128,131,132,148,
%T A372582 160,181,184,204,207,224,235,243,245,249,251,263,267,271,288,289,297,
%U A372582 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 A372582 Numbers k such that 2*k + 3 and 3*k + 2 are semiprimes.
%C A372582 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 A372582 Robert Israel, <a href="/A372582/b372582.txt">Table of n, a(n) for n = 1..10000</a>
%e A372582 a(3) = 31 is a term because 2 * 31 + 3 = 65 = 5 * 13 and 3 * 31 + 2 = 95 = 5 * 19 are both semiprimes.
%p A372582 filter:= k -> numtheory:-bigomega(3*k+2) = 2 and numtheory:-bigomega(2*k+3) = 2:
%p A372582 select(filter, [$1..1000]);
%t A372582 s = {}; Do[If[2 == PrimeOmega[2*k + 3] == PrimeOmega[3*k + 2], AppendTo[s, k]], {k, 10^3}]; s
%Y A372582 Cf. A001358.
%K A372582 nonn
%O A372582 1,1
%A A372582 _Zak Seidov_ and _Robert Israel_, May 05 2024

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