Search: id:A141174
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%I A141174
%S A141174 17,41,73,89,97,113,137,193,233,241,257,281,313,337,353,401,409,433,449,
%T A141174 457,521,569,577,593,601,617,641,673,761,769,809,857,881,929,937,953,
%U A141174 977
%N A141174 Primes of the form x^2+4*x*y-4*y^2 (as well as of the form x^2+6*x*y+y^2).
%C A141174 Discriminant = 32. 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
%C A141174 Values of the quadratic form are {0,1,4} mod 8, so this is a subset of 
               A007519. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 30 2008
%C A141174 Is this the same sequence as A007519?
%C A141174 Contribution from Tito Piezas III (tpiezas(AT)gmail.com), Dec 28 2008: 
               (Start)
%C A141174 Being a subset of A141131, this is also a subset of the primes of form 
               u^2-2v^2. (End)
%D A141174 Borevich and Shafaewich, Number Theory.
%D A141174 D. B. Zagier, Zetafunktionen und quadratische Koerper.
%e A141174 a(1)=17 because we can write 17=3^2+4*3*1-4*1^2 (or 17=1^2+6*1*2+2^2)
%Y A141174 Cf. A141175 (d=32), A007519 (Primes of form 8n+1.) A038872 (d=5). A141131 
               (d=8). A141122, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141111, 
               A141112 (d=65).
%Y A141174 Sequence in context: A126790 A089200 A004625 this_sequence A007519 A163185 
               A138005
%Y A141174 Adjacent sequences: A141171 A141172 A141173 this_sequence A141175 A141176 
               A141177
%K A141174 nonn,more
%O A141174 1,1
%A A141174 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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