A241484 Primes p such that p+2 and p+4 are semiprime.

2, 31, 47, 53, 83, 89, 139, 157, 181, 199, 211, 233, 263, 317, 337, 389, 409, 443, 449, 467, 541, 577, 587, 631, 677, 683, 719, 751, 787, 811, 839, 919, 947, 991, 1039, 1097, 1117, 1163, 1187, 1201, 1259, 1367, 1381, 1399, 1559, 1637, 1669, 1709, 1759, 1777, 1847

Offset: 1

Author

K. D. Bajpai, Apr 23 2014

Keywords

• nonn

Examples

			31 is prime and appears in the sequence because 31+2 = 33 = 3*11 and 31+4 = 35 = 5*7, which are semiprime.
53 is prime and appears in the sequence because 53+2 = 55 = 5*11 and 53+4 = 57 = 3*19, which are semiprime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A072381, A082919.

Programs

Magma

IsSemiprime:=func< p | &+[ k[2]: k in Factorization(p)] eq 2 >; [p: p in PrimesUpTo(2000)| IsSemiprime(p+2) and IsSemiprime(p+4)]; // Vincenzo Librandi, Apr 24 2014

Maple

with(numtheory): KD:= proc() local a,b,d,k; k:=ithprime(n); a:=bigomega(k+2);b:=bigomega(k+4); if a=2 and  b=2 then RETURN (k); fi; end: seq(KD(), n=1..1000);

Mathematica

KD = {}; Do[t = Prime[n];If[PrimeOmega[t + 2] == 2 && PrimeOmega[t + 4] == 2,AppendTo[KD, t]], {n, 1000}]; KD