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A141171
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Primes of the form -x^2+4*x*y+2*y^2 (as well as of the form 5*x^2+8*x*y+2*y^2).
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7
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2, 5, 23, 29, 47, 53, 71, 101, 149, 167, 173, 191, 197, 239, 263, 269, 293, 311, 317, 359, 383, 389, 431, 461, 479, 503, 509, 557, 599, 647, 653, 677, 701, 719, 743, 773, 797, 821, 839, 863, 887, 911, 941, 983, 1013, 1031, 1061, 1103, 1109, 1151, 1181, 1223, 1229, 1277, 1301, 1319, 1367
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Discriminant = 24. 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)=.
Also primes of form 6*u^2-v^2. The transformation {u,v}={y, x-2*y} yields the form in the title. - 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(4)=29 because we can write 29=-1^2+4*1*3+2*3^2 (or 29=5*1^2+8*1*2+2*2^2)
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CROSSREFS
| Cf. A141170 (d=24), A105880 (Primes for which -8 is a primitive root.) A038872 (d=5). A141131 (d=8). A141122, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141111, A141112 (d=65).
Sequence in context: A070281 A198444 A019368 * A180535 A038919 A141181
Adjacent sequences: A141168 A141169 A141170 * A141172 A141173 A141174
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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 (oscfalgan(AT)yahoo.es), Jun 12 2008
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