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Search: id:A140614
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| A140614 |
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Primes of the form 15x^2+12xy+20y^2. |
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+0
2
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| 23, 47, 71, 191, 311, 383, 599, 647, 719, 839, 863, 911, 983, 1103, 1367, 1439, 1511, 1607, 1871, 2039, 2399, 2423, 2447, 2663, 2687, 2711, 2927, 3023, 3191, 3359, 3623, 3719, 3767, 4007, 4079, 4271, 4679, 4799, 4871, 4943, 5039, 5087, 5303
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Discriminant=-1056. Also primes of the form 23x^2+12xy+36y^2.
In base 12 the sequence is 1E, 3E, 5E, 13E, 21E, 27E, 41E, 45E, 4EE, 59E, 5EE, 63E, 69E, 77E, 95E, 9EE, X5E, E1E, 10EE, 121E, 147E, 149E, 14EE, 165E, 167E, 169E, 183E, 18EE, 1X1E, 1E3E, 211E, 219E, 221E, 239E, 243E, 257E, 285E, 293E, 299E, 2X3E, 2XEE, 2E3E, 309E, where X is 10 and E is 11. Moreover, the discriminant is -740. 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), May 31 2008
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MATHEMATICA
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Union[QuadPrimes[15, 12, 20, 10000], QuadPrimes[15, -12, 20, 10000]] (* see A106856 *)
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CROSSREFS
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Cf. A140633.
Sequence in context: A130063 A141376 A134517 this_sequence A001124 A139501 A117876
Adjacent sequences: A140611 A140612 A140613 this_sequence A140615 A140616 A140617
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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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