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

1,1

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

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

Prog

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

Crossrefs

Cf. A339698.

Sequence in context: A202701 A342408 A062641 * A344732 A037424 A155088

Adjacent sequences: A339917 A339918 A339919 * A339921 A339922 A339923

Keyword

nonn

Author

Michel Marcus, Dec 23 2020

Status

approved