A092109 Primes p such that p+3 is a semiprime.

3, 7, 11, 19, 23, 31, 43, 59, 71, 79, 83, 103, 131, 139, 163, 191, 199, 211, 223, 251, 271, 311, 331, 359, 379, 383, 419, 443, 463, 479, 499, 523, 563, 619, 631, 659, 691, 743, 839, 859, 863, 883, 911, 919, 971, 1039, 1091, 1123, 1151, 1171, 1223, 1231, 1259

Offset: 1

Author

Zak Seidov, Feb 21 2004

Keywords

• easy
• nonn

Comments

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.

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

Subsequence of A131426. - Zak Seidov, Mar 29 2015

Subsequence of A091305. - David Radcliffe, May 22 2022

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

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

Programs

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

Maple

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

Mathematica

aa = {}; k = 3; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 100}]; aa (* Artur Jasinski, Oct 11 2008 *)
Select[Prime[Range[300]],PrimeOmega[#+3]==2&] (* Harvey P. Dale, Feb 07 2018 *)

PARI

is(n)=n%2 && isprime((n+3)/2) && isprime(n) \\ Charles R Greathouse IV, Jul 12 2016

Formula

a(n) = 2*A063908(n)-3 = 4*A115334(n)+3. - Artur Jasinski, Oct 11 2008