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A140620
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Primes of the form 23x^2+4xy+68y^2.
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2
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23, 263, 503, 647, 887, 1223, 1583, 1823, 1847, 2063, 2207, 2447, 2687, 2903, 3407, 3527, 3623, 3767, 4007, 4463, 4703, 4943, 4967, 5087, 5303, 5807, 5903, 5927, 6263, 6863, 7127, 7487, 7583, 7823, 8087, 8423, 8447, 9623, 9767, 10007, 10247
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OFFSET
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1,1
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COMMENTS
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Discriminant=-6240. Also primes of the form 23x^2+18xy+207y^2.
In base 12, the sequence is 1E, 19E, 35E, 45E, 61E, 85E, XEE, 107E, 109E, 123E, 133E, 14EE, 167E, 181E, 1E7E, 205E, 211E, 221E, 239E, 26EE, 287E, 2X3E, 2X5E, 2E3E, 309E, 343E, 34EE, 351E, 375E, 3E7E, 415E, 43EE, 447E, 463E, 481E, 4X5E, 4X7E, 569E, 579E, 595E, 5E1E, 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 Kehowski, Jun 01 2008
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
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MATHEMATICA
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Union[QuadPrimes[23, 4, 68, 10000], QuadPrimes[23, -4, 68, 10000]] (* see A106856 *)
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CROSSREFS
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Cf. A140633.
Sequence in context: A022618 A042018 A125411 * A002681 A142220 A142027
Adjacent sequences: A140617 A140618 A140619 * A140621 A140622 A140623
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KEYWORD
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nonn,easy
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AUTHOR
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T. D. Noe, May 19 2008
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STATUS
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approved
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