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A142955 Primes of the form 3*x^2+4*x*y-5*y^2 (as well as of the form 3*x^2+10*x*y+2*y^2). 1
2, 3, 19, 31, 59, 67, 71, 79, 103, 107, 127, 151, 167, 179, 211, 223, 227, 307, 331, 379, 383, 431, 439, 487, 523, 547, 563, 599, 607, 659, 683, 743, 751, 787, 811, 827, 839, 863, 887, 907, 911, 971, 983, 991, 1019, 1039, 1063, 1091, 1123, 1171, 1231, 1283 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Discriminant = 76. Class = 2. Binary quadratic forms a*x^2+b*x*y+c*y^2 have discriminant d=b^2-4ac and gcd(a,b,c)=1.

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..52.

EXAMPLE

a(4)=31 because we can write 31=3*3^2+4*3*2-5*2^2 (or 31=3*1^2+10*1*2+2*2^2).

CROSSREFS

Cf. A142956 (d=76). A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141111, A141112 (d=65).

Sequence in context: A265799 A058912 A040145 * A213896 A088790 A283186

Adjacent sequences:  A142952 A142953 A142954 * A142956 A142957 A142958

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 14 2008

EXTENSIONS

More terms from Colin Barker, Apr 05 2015

STATUS

approved

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Last modified November 24 07:53 EST 2020. Contains 338607 sequences. (Running on oeis4.)