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A142957 Primes of the form 3*x^2+5*x*y-6*y^2 (as well as of the form 6*x^2+11*x*y+y^2). 0
2, 3, 11, 31, 43, 47, 53, 61, 73, 79, 89, 97, 101, 103, 109, 113, 151, 163, 167, 191, 193, 197, 227, 229, 241, 269, 283, 293, 307, 313, 353, 379, 389, 397, 419, 421, 431, 449, 461, 463, 467, 479, 487, 491, 503, 509, 521, 547, 557, 571, 593, 607, 613, 617, 631 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Discriminant = 97. Class = 1. Binary quadratic forms a*x^2+b*x*y+c*y^2 have discriminant d=b^2-4ac and gcd(a,b,c)=1.

Is this the same as A038987? - R. J. Mathar, Oct 12 2013

Comment by Don Reble, Oct 06 2014 (Start):

G. B. Mathews ("Theory of Numbers" by Chelsea publishing) might have an answer to the relation with A038987. In point 59 on page 65 he claims that

- if X is a non-residue of a discriminant of a quadratic form, then X is not representable; and

- if X is a residue of D, then there is a quadratic form of determinant D which represents X.

If all forms of discriminant 97 are equivalent, then that might suffice. (Indeed, either +97 or -97 has class number 1; but I am not sure which sign matters, A003656 vs. A003173.)

(End)

REFERENCES

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

D. B. Zagier, Zetafunktionen und quadratische Koerper.

LINKS

Table of n, a(n) for n=1..55.

EXAMPLE

a(6)=47 because we can write 47=3*11^2+5*11*(-4)-6*(-4)^2 (or 47=6*2^2+11*2*1+1^2).

CROSSREFS

Cf. A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141111, A141112 (d=65).

Sequence in context: A278209 A195732 A038987 * A191058 A080155 A235625

Adjacent sequences:  A142954 A142955 A142956 * A142958 A142959 A142960

KEYWORD

nonn

AUTHOR

Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (laucabfer(AT)alum.us.es), Jul 17 2008

STATUS

approved

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Last modified April 7 01:11 EDT 2020. Contains 333291 sequences. (Running on oeis4.)