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Search: id:A007645
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| A007645 |
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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.
(Formerly M2637)
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+0
40
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| 3, 7, 13, 19, 31, 37, 43, 61, 67, 73, 79, 97, 103, 109, 127, 139, 151, 157, 163, 181, 193, 199, 211, 223, 229, 241, 271, 277, 283, 307, 313, 331, 337, 349, 367, 373, 379, 397, 409, 421, 433, 439, 457, 463, 487, 499, 523, 541, 547, 571, 577, 601, 607, 613
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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. - njas, Feb 06 2008
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REFERENCES
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D. Cox, "Primes of Form x^2 + n y^2", Wiley, 1989, p. 7.
Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 220-223, 1996.
Wagon, S. "Eisenstein Primes." Section 9.8 in Mathematica in Action. New York: W. H. Freeman, pp. 319-323, 1991.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
U. P. Nair, Elementary results on the binary quadratic form a^2+ab+b^2
Eric Weisstein's World of Mathematics, Eisenstein Integer.
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FORMULA
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p == 0 or 1 mod 3.
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CROSSREFS
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Apart from initial term, same as A045331.
Cf. A001479, A001480 (x and y such that a(n) = x^2 + 3y^2)
Adjacent sequences: A007642 A007643 A007644 this_sequence A007646 A007647 A007648
Sequence in context: A031215 A099957 A086148 this_sequence A015916 A023203 A086135
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KEYWORD
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nonn,easy
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AUTHOR
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njas, Mira Bernstein and Robert G. Wilson v (rgwv(AT)rgwv.com)
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