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
Keywords
Examples
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.
Links
- K. D. Bajpai, Table of n, a(n) for n = 1..510
Programs
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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);
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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 *) -
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