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Search: id:A084865
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| A084865 |
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Primes of the form 2x^2 + 3y^2. |
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+0
6
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| 2, 3, 5, 11, 29, 53, 59, 83, 101, 107, 131, 149, 173, 179, 197, 227, 251, 269, 293, 317, 347, 389, 419, 443, 461, 467, 491, 509, 557, 563, 587, 653, 659, 677, 683, 701, 773, 797, 821, 827, 941, 947, 971, 1013, 1019, 1061, 1091, 1109, 1163, 1181, 1187
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Subsequence of A084864; A084863(a(n))>0.
Conjecture: A084863(a(n))=1?
Is it true that a(n) = A019338(n+1)?
Comment: The truth of the conjecture A084863(a(n))=1 follows from the genus theory of quadratic forms (see Cox, page 61). By comparing enough terms, we see that the conjecture a(n) = A019338(n+1) is false. - T. D. Noe (noe(AT)sspectra.com), May 02 2008
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REFERENCES
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David A. Cox, Primes of Form x^2 + n y^2, Wiley, 1989.
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FORMULA
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The primes are congruent to {2, 3, 5, 11} (mod 24). - T. D. Noe (noe(AT)sspectra.com), May 02 2008
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EXAMPLE
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A000040(17) = 59 = 32 + 27 = 2*4^2 + 3*3^2, therefore 59 is a term.
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CROSSREFS
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Cf. A084866.
Cf. A139827.
Sequence in context: A055228 A098642 A079447 this_sequence A047934 A090235 A103596
Adjacent sequences: A084862 A084863 A084864 this_sequence A084866 A084867 A084868
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Jun 10 2003
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