A243761 Primes of the form p^2 + pq + q^2, where p and q are consecutive primes.

19, 109, 433, 1327, 4567, 6079, 19687, 49927, 62233, 103813, 160087, 172801, 238573, 363313, 395323, 463363, 583447, 640333, 753007, 1145773, 1529413, 1728247, 1968301, 2056753, 2223967, 2317927, 2349679, 2413927, 3121201, 3577393, 4148953, 4298443

Offset

1,1

Links

K. D. Bajpai, Table of n, a(n) for n = 1..8900

Example

19 is in the sequence because 2^2 + 2*3 + 3^2 = 19 is prime: 2 and 3 are consecutive primes.
109 is in the sequence because 5^2 + 5*7 + 7^2 = 109 is prime: 5 and 7 are consecutive primes.

Maple

with(numtheory): A243761:= proc() local k, p, q; p:=ithprime(n); q:=ithprime(n+1); k:=p^2 + p*q + q^2;  if isprime(k) then RETURN (k); fi; end: seq(A243761 (), n=1..500);

Mathematica

Select[Table[Prime[n]^2 + Prime[n] Prime[n + 1] + Prime[n + 1]^2, {n, 500}], PrimeQ[#] &]

Prog

(Python)
from itertools import islice
from sympy import isprime, nextprime
def A243761_gen(): # generator of terms
    p, q = 2, 3
    while True:
        if isprime(r:=p*(p+q)+q**2):
            yield r
        p, q = q, nextprime(q)
A243761_list = list(islice(A243761_gen(), 20)) # Chai Wah Wu, Feb 27 2023

Crossrefs

Cf. A000040, A007645, A003136.

Sequence in context: A264825 A142322 A306855 * A184056 A280628 A191566

Adjacent sequences: A243758 A243759 A243760 * A243762 A243763 A243764

Keyword

nonn

Author

K. D. Bajpai, Jun 10 2014

Status

approved