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A243761 Primes of the form p^2 + pq + q^2, where p and q are consecutive primes. 6
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 (list; graph; refs; listen; history; text; internal format)
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[#] &]

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

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Last modified July 2 03:39 EDT 2022. Contains 354985 sequences. (Running on oeis4.)