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Search: id:A102271
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| A102271 |
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Primes of the form 3x^2+7y^2. |
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+0
4
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| 3, 7, 19, 31, 103, 139, 199, 223, 271, 283, 307, 367, 439, 523, 607, 619, 643, 691, 727, 787, 811, 859, 1039, 1063, 1123, 1231, 1279, 1291, 1399, 1447, 1459, 1483, 1531, 1543, 1567, 1627, 1699, 1783, 1867, 1879, 1951, 1987, 2131, 2203, 2239
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Primes p such that Q(sqrt(-21p)) has genus characters chi_{-3} = +1, chi_{-7} = -1.
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REFERENCES
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Cohn, H. and Lagarias, J. C., On the existence of fields governing the 2-invariants of the classgroup of Q(sqrt{dp}) as p varies, Math. Comp. 41 (1983), 711-730.
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FORMULA
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The primes are congruent to {3, 7, 19, 31, 55} (mod 84). - T. D. Noe (noe(AT)sspectra.com), May 02 2008
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MATHEMATICA
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m=3; n=7; pLst={}; lim=3000; xMax=Sqrt[lim/m]; yMax=Sqrt[lim/n]; Do[p=m*x^2+n*y^2; If[p<lim && PrimeQ[p], AppendTo[pLst, p]], {x, xMax}, {y, yMax}]; Union[pLst] (T. D. Noe (noe(AT)sspectra.com), May 05 2005)
QuadPrimes[3, 0, 7, 10000] (* see A106856 *)
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CROSSREFS
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Cf. A102269-A102275.
Cf. A139827.
Sequence in context: A141173 A145472 A077313 this_sequence A112633 A145039 A113916
Adjacent sequences: A102268 A102269 A102270 this_sequence A102272 A102273 A102274
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Feb 19 2005
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