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Search: id:A141122
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| A141122 |
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Primes of the form x^2+2*x*y-2*y^2 (as well as of the form x^2+4*x*y+y^2). |
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+0
51
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| 13, 37, 61, 73, 97, 109, 157, 181, 193, 229, 241, 277, 313, 337, 349, 373, 397, 409, 421, 433, 457, 541, 577, 601, 613, 661, 673, 709, 733, 757, 769, 829, 853, 877, 937, 997
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Discriminant = 12. 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
Is this the same as A068228? - Artur Jasinski, Jun 09 2008
Values of the quadratic form are {0,1,4,6,9,10} mod 12, so this is a subset of A068228. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 30 2008
Are all three of A068228, A141186 and A141122 the same sequence? - njas, Sep 21 2008
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REFERENCES
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D. B. Zagier, Zetafunktionen und quadratische Koerper.
Borevich and Shafaewich, Number Theory.
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EXAMPLE
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a(1)=13 because we can write 13=3^2+2*3*1-2*1^2 (or 13=1^2+4*1*2+2^2)
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CROSSREFS
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Cf. A141123 (d=12), A068228 (Primes congruent to 1 (mod 12)) A141111, A141112 (d=65).
Adjacent sequences: A141119 A141120 A141121 this_sequence A141123 A141124 A141125
Sequence in context: A045809 A140112 A089030 this_sequence A141186 A068228 A031339
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KEYWORD
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nonn,more,new
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AUTHOR
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Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (oscfalgan(AT)yahoo.es), Jun 05 2008
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