A241483 - OEIS

%I #9 Dec 13 2018 12:25:54

%S 1381,3089,10399,49081,53759,63949,76801,98491,107509,109397,113341,

%T 143093,182747,204331,209477,239087,252949,255989,313409,396983,

%U 426287,500341,602779,677333,812281,832801,1516531,1574939,1599151,1619507,1678639,1866737,2046449

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

%H K. D. Bajpai, <a href="/A241483/b241483.txt">Table of n, a(n) for n = 1..510</a>

%e 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.

%p 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);

%t 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

%t Select[Prime[Range[155000]],Union[PrimeOmega/@(#+2Range[6])]=={2}&] (* _Harvey P. Dale_, Dec 13 2018 *)

%o (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

%o forprime(p=2,1e7,if(is(p),print1(p", "))) \\ _Charles R Greathouse IV_, Aug 25 2014

%Y Cf. A072381, A082919.

%K nonn

%O 1,1

%A _K. D. Bajpai_, Apr 23 2014