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A339920 Primes p such that p^2 - p*q + q^2 is prime, where q is the next prime after p.

%I A339920 #17 Feb 11 2021 03:03:00
%S A339920 2,3,53,151,167,263,373,443,467,509,523,571,1063,1103,1117,1217,1493,
%T A339920 1553,1901,1973,2161,2207,2281,2399,2713,2837,2963,3259,3347,3511,
%U A339920 4073,4297,4373,4463,4523,4673,4691,4877,5147,5237,5303,5419,5471,5851,6211,6311,6367
%N A339920 Primes p such that p^2 - p*q + q^2 is prime, where q is the next prime after p.
%C A339920 From _Bernard Schott_, Dec 23 2020: (Start)
%C A339920 Except for a(2)=3, (3, 5) gives A339698(2) = 19, there is no other pair of twin primes (p, p+2) (p in A001359) that gives a prime number of the form p^2-p*q+q^2 = p^2+2p+4.
%C A339920 There are no consecutive cousin primes (p, p+4) (p in A029710) that gives a prime number of the form p^2-pq+q^2 = p^2+4p+16.
%C A339920 There are no consecutive primes with a gap of 8 (p, p+8) (p in A031926) that give a prime number of the form p^2-pq+q^2 = p^2+8p+64. (End)
%H A339920 Robert Israel, <a href="/A339920/b339920.txt">Table of n, a(n) for n = 1..10000</a>
%p A339920 q:= 2: count:= 0: R:= NULL:
%p A339920 while count < 100 do
%p A339920   p:= q; q:= nextprime(q);
%p A339920   if isprime(p^2-p*q+q^2) then
%p A339920     count:= count+1; R:= R, p;
%p A339920   fi
%p A339920 od:
%p A339920 R; # _Robert Israel_, Dec 24 2020
%o A339920 (PARI) forprime(p=1, 1e4, my(q=nextprime(p+1)); if(ispseudoprime(p^2-p*q+q^2), print1(p, ", ")));
%Y A339920 Cf. A339698.
%K A339920 nonn
%O A339920 1,1
%A A339920 _Michel Marcus_, Dec 23 2020