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A140632
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Primes of the form 55x^2+10xy+199y^2.
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1
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199, 439, 1039, 1231, 1951, 2239, 2551, 2791, 3559, 3631, 4759, 5431, 6991, 7159, 7591, 8839, 9439, 10111, 11119, 11311, 11959, 13159, 13711, 13831, 14479, 14551, 15391, 15679, 15991, 16519, 16831, 17239, 17359, 17839, 17911, 18199, 18919
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Discriminant=-43680. Also primes of the form 159x^2+120xy+160y^2.
In base 12, the sequence is 147, 307, 727, 867, 1167, 1367, 1587, 1747, 2087, 2127, 2907, 3187, 4067, 4187, 4487, 5147, 5567, 5X27, 6527, 6667, 6E07, 7747, 7E27, 8007, 8467, 8507, 8XX7, 90X7, 9307, 9687, 98X7, 9E87, X067, X3X7, X447, X647, XE47, 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
| Union[QuadPrimes[55, 10, 199, 10000], QuadPrimes[55, -10, 199, 10000]] (* see A106856 *)
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CROSSREFS
| Cf. A140633.
Sequence in context: A004946 A157955 A033168 * A142814 A105975 A095995
Adjacent sequences: A140629 A140630 A140631 * A140633 A140634 A140635
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KEYWORD
| nonn,easy
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), May 19 2008
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