cp's OEIS Frontend

A243904 Semiprimes of the form p^2 + pq + q^2, where p, q are consecutive primes.

%I A243904 #11 Jun 25 2022 17:08:00
%S A243904 49,247,679,973,2701,5293,7509,10801,12297,15553,17337,25963,29407,
%T A243904 33079,34993,36967,43249,53877,67501,71157,76809,97201,117613,155953,
%U A243904 181573,225237,270049,292033,297679,314977,350917,380217,477607,492091,514213,632047,648679
%N A243904 Semiprimes of the form p^2 + pq + q^2, where p, q are consecutive primes.
%C A243904 Intersection of A001358 and A003136.
%H A243904 K. D. Bajpai, <a href="/A243904/b243904.txt">Table of n, a(n) for n = 1..10000</a>
%e A243904 247 is in the sequence because 7^2 + 7*11 + 11^2 = 247 = 13*19, which is semiprime.
%e A243904 679 is in the sequence because 13^2 + 13*17 + 17^2 = 679 = 7*97, which is semiprime.
%p A243904 with(numtheory): A243904:= proc() local k, p, q; p:=ithprime(n); q:=ithprime(n+1); k:=p^2 + p*q + q^2;  if bigomega(k)=2 then RETURN (k); fi; end: seq(A243904 (), n=1..200);
%t A243904 Select[Table[Prime[n]^2 + Prime[n] Prime[n + 1] + Prime[n + 1]^2, {n, 100}], PrimeOmega[#] == 2 &]
%o A243904 (PARI) issemi(n)=bigomega(n)==2
%o A243904 list(lim)=my(v=List(),p=3,t); forprime(q=5,, t=p^2+p*q+q^2; if(t>lim, break); if(issemi(t), listput(v,t)); p=q); Vec(v) \\ _Charles R Greathouse IV_, Jul 05 2017
%Y A243904 Cf. A001358, A007945, A003136, A243761.
%K A243904 nonn
%O A243904 1,1
%A A243904 _K. D. Bajpai_, Jun 14 2014