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A140623
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Primes of the form 35x^2+30xy+51y^2.
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131, 179, 251, 419, 491, 659, 971, 1091, 1499, 1811, 1979, 2339, 2531, 2939, 3251, 3299, 3371, 3539, 3779, 3851, 4091, 4211, 4931, 5099, 5171, 5651, 6491, 6659, 6899, 6971, 7019, 7211, 7331, 8219, 8291, 9491, 9539, 9851, 10091, 10139, 10331
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Discriminant=-6240. Also primes of the form 36x^2+12xy+131y^2.
In base 12, the sequence is XE, 12E, 18E, 2XE, 34E, 46E, 68E, 76E, X4E, 106E, 118E, 142E, 156E, 184E, 1X6E, 1XXE, 1E4E, 206E, 222E, 228E, 244E, 252E, 2X2E, 2E4E, 2EXE, 332E, 390E, 3X2E, 3EXE, 404E, 408E, 420E, 42XE, 490E, 496E, 55XE, 562E, 584E, 5X0E, 5X4E, 5E8E, where X is 10 and E is 11. Moreover, the discriminant is -3740. 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[35, 30, 51, 10000], QuadPrimes[35, -30, 51, 10000]] (* see A106856 *)
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CROSSREFS
| Cf. A140633.
Sequence in context: A090264 A132254 A087832 * A050261 A180544 A032750
Adjacent sequences: A140620 A140621 A140622 * A140624 A140625 A140626
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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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