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A241483 Primes p such that p+2, p+4, p+6, p+8, p+10 and p+12 are all semiprime. 7
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 17 19:44 EDT 2019. Contains 328128 sequences. (Running on oeis4.)