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Search: id:A140618
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| A140618 |
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Primes of the form 20x^2+4xy+23y^2. |
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1
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| 23, 47, 191, 239, 263, 311, 359, 479, 503, 647, 719, 1031, 1103, 1151, 1223, 1487, 1559, 1583, 1607, 1847, 1871, 2039, 2063, 2087, 2399, 2543, 2591, 2927, 2999, 3407, 3671, 3767, 3863, 3911, 4007, 4127, 4463, 4583, 4679, 4751, 4799, 4871
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Discriminant=-1824. Also primes of the form 23x^2+20xy+44y^2.
In base 12, the sequence is 1E, 3E, 13E, 17E, 19E, 21E, 25E, 33E, 35E, 45E, 4EE, 71E, 77E, 7EE, 85E, X3E, X9E, XEE, E1E, 109E, 10EE, 121E, 123E, 125E, 147E, 157E, 15EE, 183E, 189E, 1E7E, 215E, 221E, 229E, 231E, 239E, 247E, 26EE, 279E, 285E, 28EE, 293E, 299E, where X is for 10 and E is for 11. Moreover, the discriminant is -1080. 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[20, 4, 23, 10000], QuadPrimes[20, -4, 23, 10000]] (* see A106856 *)
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CROSSREFS
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Cf. A140633.
Sequence in context: A139857 A139900 A065017 this_sequence A042052 A136030 A054693
Adjacent sequences: A140615 A140616 A140617 this_sequence A140619 A140620 A140621
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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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