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Search: id:A140631
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| A140631 |
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Primes of the form 57x^2+18xy+193y^2. |
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+0
1
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| 193, 457, 1033, 2017, 2137, 2377, 3217, 3313, 3697, 4153, 5233, 6073, 6337, 7057, 7417, 7753, 8353, 9433, 10753, 11113, 11617, 11953, 12097, 12433, 12553, 13297, 14737, 15073, 16417, 16633, 16993, 17257, 17977, 19273, 20113, 20353, 20857
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Discriminant=-43680. Also primes of the form 148x^2+132xy+177y^2.
In base 12, the sequence is 141, 321, 721, 1201, 12X1, 1461, 1X41, 1E01, 2181, 24X1, 3041, 3621, 3801, 4101, 4361, 45X1, 4X01, 5561, 6281, 6521, 6881, 6E01, 7001, 7241, 7321, 7841, 8641, 8881, 9601, 9761, 9X01, 9EX1, X4X1, E1X1, E781, E941, 100X1, where X is 10 and E is 11. Moreover, the discriminant is -21340. Keep in mind that 12 is a canonical base for mathematics in general since any prime greater than 3 is of the form 6k+-1, any prime of the form 4k+1 is a sum of squares while any prime of the form 4k+3 is never a sum of squares and lcm(6,4)=12. - Walter A. Kehowski (wkehowski(AT)cox.net), Jun 01 2008
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MATHEMATICA
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Union[QuadPrimes[57, 18, 193, 10000], QuadPrimes[57, -18, 193, 10000]] (* see A106856 *)
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CROSSREFS
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Cf. A140633.
Sequence in context: A142500 A113000 A105129 this_sequence A142117 A142564 A125647
Adjacent sequences: A140628 A140629 A140630 this_sequence A140632 A140633 A140634
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KEYWORD
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nonn,easy
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), May 19 2008
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