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Primes of the form -x^2 + 8*x*y + 8*y^2 (as well as of the form 15*x^2 + 24*x*y + 8*y^2).
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%I #24 Feb 18 2022 16:06:07

%S 23,47,71,167,191,239,263,311,359,383,431,479,503,599,647,719,743,839,

%T 863,887,911,983,1031,1103,1151,1223,1319,1367,1439,1487,1511,1559,

%U 1583,1607,1823,1847,1871,2039,2063,2087,2111,2207,2351,2399,2423,2447,2543

%N Primes of the form -x^2 + 8*x*y + 8*y^2 (as well as of the form 15*x^2 + 24*x*y + 8*y^2).

%C Discriminant = +96.

%C Values of the quadratic form are {0, 8, 12, 15, 20, 23} mod 24, so this is a subsequence of A134517. - _R. J. Mathar_, Jul 30 2008

%C Is this the same sequence as A134517?

%C Substituting 2y = y' gives the quadratic form A141171, so these terms are a subsequence of the terms in A141171. - _R. J. Mathar_, Jun 10 2020

%D Z. I. Borevich and I. R. Shafarevich, Number Theory.

%H N. J. A. Sloane et al., <a href="/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a>: Index to related sequences, programs, references. OEIS wiki, June 2014.

%H D. B. Zagier, <a href="https://doi.org/10.1007/978-3-642-61829-1">Zetafunktionen und quadratische Körper</a>, Springer, 1981.

%e a(2)=47 because we can write 47 = -1^2 + 8*1*2 + 8*2^2 (or 47 = 15*1^2 + 24*1*1 + 8*1^2).

%Y Cf. A107003, A134517, A141171, A141373, A141375 (d = -96).

%K nonn

%O 1,1

%A Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (oscfalgan(AT)yahoo.es), Jun 28 2008

%E More terms from _Arkadiusz Wesolowski_, Jul 25 2012