cp's OEIS Frontend

A243544 Primes p such that p^2 - p + 1 is semiprime.

%I A243544 #13 Oct 22 2024 14:32:47
%S A243544 5,11,29,37,41,43,53,61,71,73,83,97,109,113,127,137,149,157,167,181,
%T A243544 191,211,223,229,241,271,277,281,307,317,331,359,389,421,433,443,461,
%U A243544 463,487,499,547,557,571,587,601,617,631,659,661,683,691,701,709,733,757
%N A243544 Primes p such that p^2 - p + 1 is semiprime.
%C A243544 Intersection of A000040 and A180748.
%H A243544 K. D. Bajpai, <a href="/A243544/b243544.txt">Table of n, a(n) for n = 1..7090</a>
%e A243544 11 is in the sequence because 11 is prime and 11^2 - 11 + 1 = 111 = 3 * 37 is semiprime.
%e A243544 29 is in the sequence because 29 is prime and 29^2 - 29 + 1 = 813 = 3 * 271 is semiprime.
%e A243544 17 is not in the sequence though 17 is prime, because 17^2 - 17 + 1 = 273 = 3 * 7 * 13, has more than two prime factors.
%p A243544 with(numtheory): A243544 := proc() local a; a:=ithprime(n);  if bigomega(a^2-a+1)=2 then RETURN (a); fi; end: seq(A243544 (), n=1..200);
%t A243544 c = 0; Do[k = Prime[n]; If[PrimeOmega[k^2 - k + 1] == 2, c++; Print[c, " ", k]], {n, 1, 30000}];
%t A243544 Select[Prime[Range[150]],PrimeOmega[#^2-#+1]==2&] (* _Harvey P. Dale_, Oct 22 2024 *)
%o A243544 (PARI) s=[]; forprime(p=2, 800, if(bigomega(p^2-p+1)==2, s=concat(s, p))); s \\ _Colin Barker_, Jun 06 2014
%Y A243544 Cf. A000040, A001358, A053182, A053184, A065508, A091567, A180748.
%K A243544 nonn
%O A243544 1,1
%A A243544 _K. D. Bajpai_, Jun 06 2014