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A140625
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Primes of the form 28x^2+20xy+85y^2.
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157, 277, 397, 613, 733, 757, 853, 997, 1213, 1453, 1597, 2053, 2437, 2557, 2677, 2797, 3037, 3253, 3733, 3877, 4357, 4813, 4957, 5077, 5413, 5557, 6277, 6637, 6733, 6997, 7237, 7573, 8053, 8293, 8893, 9013, 9277, 9397, 9733, 9973, 10093
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Discriminant=-9120. Also primes of the form 45x^2+30xy+157y^2.
In base 12, the sequence is 111, 1E1, 291, 431, 511, 531, 5E1, 6E1, 851, X11, E11, 1231, 14E1, 1591, 1671, 1751, 1911, 1X71, 21E1, 22E1, 2631, 2951, 2X51, 2E31, 3171, 3271, 3771, 3X11, 3X91, 4071, 4231, 4471, 47E1, 4971, 5191, 5271, 5451, 5531, 5771, 5931, 5X11, where X is 10 and E is 11. Moreover, the discriminant is -5340. 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[28, 20, 85, 10000], QuadPrimes[28, -20, 85, 10000]] (* see A106856 *)
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CROSSREFS
| Cf. A140633.
Sequence in context: A142367 A001837 A142581 * A142874 A060974 A073277
Adjacent sequences: A140622 A140623 A140624 * A140626 A140627 A140628
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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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