A141376 - OEIS

A141376

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).

23, 47, 71, 167, 191, 239, 263, 311, 359, 383, 431, 479, 503, 599, 647, 719, 743, 839, 863, 887, 911, 983, 1031, 1103, 1151, 1223, 1319, 1367, 1439, 1487, 1511, 1559, 1583, 1607, 1823, 1847, 1871, 2039, 2063, 2087, 2111, 2207, 2351, 2399, 2423, 2447, 2543

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OFFSET

1,1

COMMENTS

Discriminant = +96.

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

Is this the same sequence as A134517?

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

REFERENCES

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

LINKS

Table of n, a(n) for n=1..47.

N. J. A. Sloane et al., Binary Quadratic Forms and OEIS: Index to related sequences, programs, references. OEIS wiki, June 2014.

D. B. Zagier, Zetafunktionen und quadratische Körper, Springer, 1981.

EXAMPLE

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).

CROSSREFS

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

Sequence in context: A130063 A183010 A134517 * A140614 A001124 A139501

Adjacent sequences: A141373 A141374 A141375 * A141377 A141378 A141379

KEYWORD

nonn

AUTHOR

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

EXTENSIONS

More terms from Arkadiusz Wesolowski, Jul 25 2012

STATUS

approved