A243365 - OEIS

%I #21 Jul 08 2014 17:30:38

%S 101,157,173,229,233,239,347,349,353,421,439,479,521,577,619,661,719,

%T 751,761,829,881,1019,1061,1117,1129,1153,1277,1289,1321,1447,1453,

%U 1489,1523,1579,1721,1733,1801,1811,1823,1831,1861,1871,1873,2027,2099,2221,2239

%N Primes p such that both p^2 + 6 and p^2 - 6 are semiprime.

%H K. D. Bajpai, <a href="/A243365/b243365.txt">Table of n, a(n) for n = 1..10000</a>

%e 101 is in the sequence because 101 is prime. 101^2 + 6 = 10207 = 59 * 173 which is semiprime. 101^2 - 6 = 10195 = 5 * 2039 which is semiprime.

%e 157 is in the sequence because 157 is prime. 157^2 + 6 = 24655 = 5 * 4931 which is semiprime. 157^2 - 6 = 24643 = 19 * 1297 which is semiprime.

%p with(numtheory): A243365:= proc()local k; k:=ithprime(n); if bigomega(k^2+6)=2 and bigomega(k^2-6)=2 then RETURN (k); fi; end: seq(A243365 (),n=1..5000);

%t A243365 = {}; k = Prime[n]; Do[If[PrimeOmega[k^2 + 6] == 2 && PrimeOmega[k^2 - 6] == 2, AppendTo[A243365, k]], {n, 1000}]; A243365

%t Select[Prime[Range[400]],PrimeOmega[#^2+{6,-6}]=={2,2}&] (* _Harvey P. Dale_, Jul 08 2014 *)

%o (PARI) s=[]; forprime(p=2, 3000, if(bigomega(p^2+6)==2 && bigomega(p^2-6)==2, s=concat(s, p))); s \\ _Colin Barker_, Jun 25 2014

%Y Cf. A000040 (primes), A001358 (semiprimes).

%Y Cf. A117328 (p+/-4 semiprime), A115395(p+/-6 semiprime), A242244 (p^2+/-2 semiprime).

%K nonn

%O 1,1

%A _K. D. Bajpai_, Jun 24 2014