%I #34 May 22 2022 14:02:49

%S 3,7,11,19,23,31,43,59,71,79,83,103,131,139,163,191,199,211,223,251,

%T 271,311,331,359,379,383,419,443,463,479,499,523,563,619,631,659,691,

%U 743,839,859,863,883,911,919,971,1039,1091,1123,1151,1171,1223,1231,1259

%N Primes p such that p+3 is a semiprime.

%C Primes p such that p-3 is semiprime are in A089531; p and 2p+3 both prime, A023204; p, 2p-3 and 2p+3 prime, A092110.

%C Primes p such that (p+3)/2 is prime. All these primes are congruent to 3 mod 4. - _Artur Jasinski_, Oct 11 2008

%C Subsequence of A131426. - _Zak Seidov_, Mar 29 2015

%C Subsequence of A091305. - _David Radcliffe_, May 22 2022

%H Vincenzo Librandi, <a href="/A092109/b092109.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = 2*A063908(n)-3 = 4*A115334(n)+3. - _Artur Jasinski_, Oct 11 2008

%p select(p -> isprime(p) and isprime((p+3)/2), [seq(2*k+1,k=1..1000)]); # _Robert Israel_, Mar 29 2015

%t aa = {}; k = 3; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 100}]; aa (* _Artur Jasinski_, Oct 11 2008 *)

%t Select[Prime[Range[300]],PrimeOmega[#+3]==2&] (* _Harvey P. Dale_, Feb 07 2018 *)

%o (Magma) IsSemiprime:=func< p | &+[ k[2]: k in Factorization(p)] eq 2 >; [p: p in PrimesUpTo(1300)| IsSemiprime(p+3)]; // _Vincenzo Librandi_, Feb 21 2014

%o (PARI) is(n)=n%2 && isprime((n+3)/2) && isprime(n) \\ _Charles R Greathouse IV_, Jul 12 2016

%Y Cf. A023204, A089531, A063908, A092110, A115334, A131426.

%K easy,nonn

%O 1,1

%A _Zak Seidov_, Feb 21 2004