Search: id:A007645
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%I A007645 M2637
%S A007645 3,7,13,19,31,37,43,61,67,73,79,97,103,109,127,139,151,157,163,181,
%T A007645 193,199,211,223,229,241,271,277,283,307,313,331,337,349,367,373,379,
%U A007645 397,409,421,433,439,457,463,487,499,523,541,547,571,577,601,607,613
%N A007645 Cuban primes: primes of the form x^2 + xy + y^2; or: primes of form x^2 
               + 3*y^2; or: primes == 0 or 1 mod 3.
%C A007645 These are not to be confused with the Eisenstein primes, which are the 
               primes in the ring of integers Z[w], where w = (-1+sqrt(-3))/2. The 
               present sequence gives the rational primes which are also Eisenstein 
               primes. - N. J. A. Sloane (njas(AT)research.att.com), Feb 06 2008
%C A007645 Also primes of the form x^2+3y^2 and, except for 3, x^2+xy+7y^2. See 
               A140633. - T. D. Noe (noe(AT)sspectra.com), May 19 2008
%C A007645 Conjecture: this sequence is Union(A002383,A162471). [From Daniel Tisdale 
               (daniel6874(AT)gmail.com), Jul 04 2009]
%D A007645 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A007645 D. Cox, "Primes of Form x^2 + n y^2", Wiley, 1989, p. 7.
%D A007645 Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, 
               pp. 220-223, 1996.
%D A007645 Wagon, S. "Eisenstein Primes." Section 9.8 in Mathematica in Action. 
               New York: W. H. Freeman, pp. 319-323, 1991.
%H A007645 T. D. Noe, <a href="b007645.txt">Table of n, a(n) for n=1..1000</a>
%H A007645 U. P. Nair, <a href="http://arXiv.org/abs/math.NT/0408107">Elementary 
               results on the binary quadratic form a^2+ab+b^2</a>
%H A007645 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               EisensteinInteger.html">Eisenstein Integer.</a>
%F A007645 p == 0 or 1 mod 3.
%F A007645 {3} UNION A002476. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Oct 28 2008]
%t A007645 Clear[f,lst,p,x,y]; f[x_,y_]:=x^2+x*y+y^2; lst={};Do[Do[p=f[x,y];If[PrimeQ[p]&&p<3614,
               AppendTo[lst,p]],{y,0,3*5!}],{x,0,3*5!}];Take[Union[lst],250] [From 
               Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 04 2009]
%Y A007645 Apart from initial term, same as A045331.
%Y A007645 Cf. A001479, A001480 (x and y such that a(n) = x^2 + 3y^2)
%Y A007645 Sequence in context: A099957 A086148 A167462 this_sequence A144919 A015916 
               A023203
%Y A007645 Adjacent sequences: A007642 A007643 A007644 this_sequence A007646 A007647 
               A007648
%K A007645 nonn,easy
%O A007645 1,1
%A A007645 N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein and Robert 
               G. Wilson v (rgwv(AT)rgwv.com)

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