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A141778 Primes of the form 4*x^2+3*x*y-5*y^2 (as well as of the form 8*x^2+11*x*y+y^2). 2
2, 5, 11, 17, 47, 53, 67, 71, 73, 79, 89, 97, 107, 109, 131, 139, 157, 167, 173, 179, 199, 223, 227, 233, 251, 257, 263, 269, 271, 277, 283, 307, 311, 317, 331, 347, 367, 373, 401, 409, 443, 449, 461, 463, 467, 479, 487, 509, 523, 587, 601, 607, 613, 619, 631 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Discriminant = 89. 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 A038977? - R. J. Mathar, Jul 04 2008

A subsequence of (and may possibly coincide with) A038977. - R. J. Mathar, Jul 22 2008

REFERENCES

Borevich and Shafaewich, Number Theory.

D. B. Zagier, Zetafunktionen und quadratische Koerper.

LINKS

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

EXAMPLE

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

CROSSREFS

See also A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141158 (d=20). A141159, A141160 (d=21). A141170, A141171 (d=24). A141172, A141173 (d=28). A141174, A141175 (d=32). A141176, A141177 (d=33). A141178 (d=37). A141179, A141180 (d=40). A141181 (d=41). A141182, A141183 (d=44). A033212, A141185 (d=45). A068228, A141187 (d=48). A141188 (d=52). A141189 (d=53). A141190, A141191 (d=56). A141192, A141193 (d=57). A141301, A141302, A141303, A141304 (d=60). A141215 (d=61). A141111, A141112 (d=65). A141750 (d=73). A141772, A141773 (d=85). A141776, A141777 (d=88). A141778 (d=89). A141161, A141162, A141163 (d=148). A141165, A141166 (d=229). A141167, A141168 (d=257).

Sequence in context: A174003 A144572 A038977 * A191053 A209493 A117877

Adjacent sequences:  A141775 A141776 A141777 * A141779 A141780 A141781

KEYWORD

nonn

AUTHOR

Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (sergarmor(AT)yahoo.es), Jul 04 2008

STATUS

approved

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Last modified December 20 22:17 EST 2014. Contains 252289 sequences.