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A242708 Primes p such that p^2 + p + 41 is semiprime.

%I A242708 #8 May 21 2014 20:07:44
%S A242708 41,89,109,127,163,173,239,251,271,283,331,347,349,367,373,383,389,
%T A242708 401,409,421,443,449,463,467,487,547,557,563,569,571,577,587,593,613,
%U A242708 643,661,701,727,733,739,761,769,773,797,823,827,853,857,881,907,937,947,971
%N A242708 Primes p such that p^2 + p + 41 is semiprime.
%C A242708 n^2+n+41 is sometimes referred to as Euler's polynomial.
%C A242708 Subsequence of A228184.
%C A242708 A242702 is for semiprimes such that n^2+n+41 is also semiprime.
%H A242708 K. D. Bajpai, <a href="/A242708/b242708.txt">Table of n, a(n) for n = 1..10000</a>
%e A242708 41 is prime and 41^2 + 41 + 41 = 1763 = 41 * 43 is semiprime. Hence, 41 is in the sequence.
%e A242708 127 is prime and 127^2 + 127 + 41 = 16297 = 43 * 379 is semiprime. Hence, 127 is in the sequence.
%e A242708 43 is prime and 43^2 + 43 + 41 = 1933 which is prime (not semiprime). Hence, 43 is not in the sequence.
%p A242708 with(numtheory): A242708:= proc();  if isprime(n) and bigomega(n^2+n+41)=2 then RETURN (n);  fi;  end: seq(A242708 (), n=1..1000);
%t A242708 c = 0; Do[If[PrimeQ[n] && PrimeOmega[n^2 + n + 41] == 2, c++; Print[c, "  ", n]], {n, 1, 3*10^5}];
%Y A242708 Cf. A000040, A001358, A228184, A238242, A242702.
%K A242708 nonn
%O A242708 1,1
%A A242708 _K. D. Bajpai_, May 21 2014