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A328137 Primes p such that p+1 is the product of two distinct primes and p+2 is the product of three distinct primes.

%I A328137 #18 Sep 08 2022 08:46:24
%S A328137 193,397,613,661,757,1093,1237,1453,1657,2137,2341,2593,2917,3217,
%T A328137 4177,4621,5233,6121,6133,7057,7537,8101,8317,8353,8677,8893,9013,
%U A328137 9721,10957,11677,11701,12421,12433,12541,12853,13933,15277,15733,16033,16381,16417,16633,17257,17293,18013,18253,18481
%N A328137 Primes p such that p+1 is the product of two distinct primes and p+2 is the product of three distinct primes.
%C A328137 All terms == 1 (mod 12).
%C A328137 Members k of A112998 such that k+2 is squarefree.
%H A328137 Robert Israel, <a href="/A328137/b328137.txt">Table of n, a(n) for n = 1..10000</a>
%e A328137 a(3)=613 is in the sequence because 613 is prime, 614=2*307 is the product of two distinct primes, and 615=3*5*41 is the product of three distinct primes.
%p A328137 select(t -> isprime(t) and isprime((t+1)/2) and numtheory:-issqrfree(t+2) and numtheory:-bigomega(t+2)=3, [seq(i,i=1..10^5,12)]);
%o A328137 (Magma) [p:p in PrimesUpTo(20000)| IsPrime((p+1) div 2) and IsSquarefree(p+2) and #PrimeDivisors(p+2) eq 3]; // _Marius A. Burtea_, Oct 04 2019
%Y A328137 Contained in A005383, A100363 and A112998.
%K A328137 nonn
%O A328137 1,1
%A A328137 _J. M. Bergot_ and _Robert Israel_, Oct 04 2019