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

1,1

Links

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

Example

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.

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

Prog

(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

Crossrefs

Cf. A072381, A082919.

Sequence in context: A101017 A207973 A193423 * A235477 A370157 A129900

Adjacent sequences: A241481 A241482 A241483 * A241485 A241486 A241487

Keyword

nonn

Author

K. D. Bajpai, Apr 23 2014

Status

approved