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A140630
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Primes of the form 88x^2+32xy+127y^2.
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127, 823, 1303, 1327, 1663, 3823, 3847, 3943, 4447, 4663, 4783, 5503, 6007, 6343, 6367, 6967, 7687, 8527, 8863, 10663, 10903, 11047, 11743, 12583, 13183, 14407, 14767, 15583, 16927, 17047, 18223, 19447, 20407, 20983, 23143, 23167, 23767
(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 127x^2+4xy+172y^2.
In base 12, the sequence is X7, 587, 907, 927, E67, 2267, 2287, 2347, 26X7, 2847, 2927, 3227, 3587, 3807, 3827, 4047, 4547, 4E27, 5167, 6207, 6387, 6487, 6967, 7347, 7767, 8407, 8667, 9027, 9967, 9X47, X667, E307, E987, 10187, 11487, 114X7, 11907, 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[88, 32, 127, 10000], QuadPrimes[88, -32, 127, 10000]] (* see A106856 *)
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CROSSREFS
| Cf. A140633.
Sequence in context: A049202 A204737 A060201 * A183829 A168487 A075942
Adjacent sequences: A140627 A140628 A140629 * A140631 A140632 A140633
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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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