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

2, 3, 53, 151, 167, 263, 373, 443, 467, 509, 523, 571, 1063, 1103, 1117, 1217, 1493, 1553, 1901, 1973, 2161, 2207, 2281, 2399, 2713, 2837, 2963, 3259, 3347, 3511, 4073, 4297, 4373, 4463, 4523, 4673, 4691, 4877, 5147, 5237, 5303, 5419, 5471, 5851, 6211, 6311, 6367

Offset: 1

Author

Michel Marcus, Dec 23 2020

Keywords

• nonn

Comments

From Bernard Schott, Dec 23 2020: (Start)

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.

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.

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)

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A339698.

Programs

Maple

q:= 2: count:= 0: R:= NULL:
while count < 100 do
  p:= q; q:= nextprime(q);
  if isprime(p^2-p*q+q^2) then
    count:= count+1; R:= R, p;
  fi
od:
R; # Robert Israel, Dec 24 2020

PARI

forprime(p=1, 1e4, my(q=nextprime(p+1)); if(ispseudoprime(p^2-p*q+q^2), print1(p, ", ")));