A241483 Primes p such that p+2, p+4, p+6, p+8, p+10 and p+12 are all semiprime.

1381, 3089, 10399, 49081, 53759, 63949, 76801, 98491, 107509, 109397, 113341, 143093, 182747, 204331, 209477, 239087, 252949, 255989, 313409, 396983, 426287, 500341, 602779, 677333, 812281, 832801, 1516531, 1574939, 1599151, 1619507, 1678639, 1866737, 2046449

Offset

1,1

Links

K. D. Bajpai, Table of n, a(n) for n = 1..510

Example

1381 is prime and appears in the sequence because 1381+2 = 1383 = 3*461, 1381+4 = 1385 = 5*277, 1381+6 = 1387 = 19*73, 1381+8 = 1389 = 3*463, 1381+10 = 1391 = 13*107 and  1381+12 = 1393 = 7*199, which are all semiprime.

Maple

with(numtheory): KD:= proc() local a, b, d, e, f, g, k; k:=ithprime(n); a:=bigomega(k+2); b:=bigomega(k+4); d:=bigomega(k+6);  e:=bigomega(k+8); f:=bigomega(k+10); g:=bigomega(k+12);  if a=2 and  b=2 and  d=2 and  e=2 and  f=2 and  g=2then RETURN (k);  fi; end: seq(KD(), n=1..200000);

Mathematica

KD = {};  Do[t = Prime[n]; If[PrimeOmega[t + 2] == 2 && PrimeOmega[t + 4] == 2 && PrimeOmega[t + 6] == 2 && PrimeOmega[t + 8] == 2 && PrimeOmega[t + 10] == 2 && PrimeOmega[t + 12] == 2, AppendTo[KD, t]], {n, 200000}]; KD
Select[Prime[Range[155000]], Union[PrimeOmega/@(#+2Range[6])]=={2}&] (* Harvey P. Dale, Dec 13 2018 *)

Prog

(PARI) is(n)=if(n%3==1, isprime((n+2)/3) && isprime((n+8)/3) && bigomega(n+4)==2 && bigomega(n+10)==2, isprime((n+4)\3) && isprime((n+10)\3) && bigomega(n+2)==2 && bigomega(n+8)==2) && isprime(n) && bigomega(n+6)==2 && bigomega(n+12)==2
forprime(p=2, 1e7, if(is(p), print1(p", "))) \\ Charles R Greathouse IV, Aug 25 2014

Crossrefs

Cf. A072381, A082919.

Sequence in context: A031796 A020406 A277632 * A134671 A161192 A134670

Adjacent sequences: A241480 A241481 A241482 * A241484 A241485 A241486

Keyword

nonn

Author

K. D. Bajpai, Apr 23 2014

Status

approved