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A141177
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Primes of the form -2*x^2+3*x*y+3*y^2 (as well as of the form 4*x^2+7*x*y+y^2).
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7
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3, 31, 37, 67, 97, 103, 157, 163, 181, 199, 223, 229, 313, 331, 367, 379, 397, 421, 433, 463, 487, 499, 577, 619, 631, 643, 661, 691, 709, 727, 751, 757, 823, 829, 859, 883, 907, 991, 1021, 1039, 1087, 1093, 1123, 1153, 1171, 1213, 1237, 1279, 1291, 1303, 1321, 1423, 1453, 1483
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Discriminant = 33. 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
It is true that A141177(n+1)=A107013(n)?. That is: except for p=3 are these the primes represented by x^2-x*y+25*y^2 with x, y nonnegative? - Juan Arias-de-Reyna, Mar 19 2011
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REFERENCES
| Borevich and Shafaewich, Number Theory.
D. B. Zagier, Zetafunktionen und quadratische Koerper.
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LINKS
| Juan Arias-de-Reyna, Table of n, a(n) for n = 1..10000
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EXAMPLE
| a(2)=31 because we can write 31=-2*4^2+3*4*3+3*3^2 (or 31=4*2^2+7*2*1+1^2)
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CROSSREFS
| Cf. A141176 (d=33) A038872 (d=5). A141131 (d=8). A141122, A141123 (d=12). A038883 (d=13). A038889 (d=17): A141111, A141112 (d=65).
Sequence in context: A023297 A077546 A168274 * A154502 A046282 A045709
Adjacent sequences: A141174 A141175 A141176 * A141178 A141179 A141180
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KEYWORD
| nonn
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AUTHOR
| Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (marcanmar(AT)alum.us.es), Jun 12 2008
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