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A141338 Primes of the form x^2+9*x*y-3*y^2 (as well as of the form 7*x^2+11*x*y+y^2). 2
7, 19, 31, 67, 97, 103, 109, 157, 163, 193, 211, 283, 307, 349, 373, 379, 397, 421, 439, 541, 547, 577, 607, 661, 691, 727, 733, 751, 769, 811, 853, 877, 907, 919, 937, 997, 1033, 1039, 1051, 1063, 1087, 1093, 1117, 1123, 1213, 1237, 1249, 1279, 1291, 1303 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Discriminant = 93. 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

Borevich and Shafaewich, Number Theory.

D. B. Zagier, Zetafunktionen und quadratische Koerper.

LINKS

Table of n, a(n) for n=1..50.

EXAMPLE

a(2)=19 because we can write 19=2^2+9*2*5-3*5^2 (or 19=7*1^2+11*1*1+1^2).

CROSSREFS

Cf. A141339 (d=93).

Sequence in context: A249375 A212492 A234310 * A237366 A216531 A216564

Adjacent sequences:  A141335 A141336 A141337 * A141339 A141340 A141341

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 25 2008

EXTENSIONS

More terms from Colin Barker, Apr 05 2015

STATUS

approved

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Last modified June 15 19:32 EDT 2019. Contains 324144 sequences. (Running on oeis4.)