

A339920


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


3



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
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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^2p*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^2pq+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^2pq+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^2p*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^2p*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



