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Search: id:A140615
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| A140615 |
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Primes of the form 13x^2+6xy+21y^2. |
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+0
2
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| 13, 61, 109, 277, 349, 373, 541, 613, 733, 853, 877, 997, 1069, 1117, 1381, 1429, 1597, 1669, 1693, 1789, 1861, 1933, 2053, 2221, 2389, 2437, 2749, 2917, 3109, 3181, 3229, 3253, 3373, 3517, 3541, 3637, 3709, 4021, 4549, 4597, 4813, 4861
(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 13x^2+2xy+61y^2.
In base 12, the sequence is 11, 51, 91, 1E1, 251, 271, 391, 431, 511, 5E1, 611, 6E1, 751, 791, 971, 9E1, E11, E71, E91, 1051, 10E1, 1151, 1231, 1351, 1471, 14E1, 1711, 1831, 1971, 1X11, 1X51, 1X71, 1E51, 2051, 2071, 2131, 2191, 23E1, 2771, 27E1, 2951, 2991, 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[13, 6, 21, 10000], QuadPrimes[13, -6, 21, 10000]] (* see A106856 *)
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CROSSREFS
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Cf. A140633.
Adjacent sequences: A140612 A140613 A140614 this_sequence A140616 A140617 A140618
Sequence in context: A028874 A087106 A142402 this_sequence A086361 A119151 A081589
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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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