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A140613
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Primes of the form 7x^2+6xy+39y^2.
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1
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7, 79, 127, 151, 271, 439, 607, 919, 967, 1063, 1231, 1327, 1399, 1447, 1471, 1663, 1759, 1999, 2239, 2287, 2383, 2503, 2551, 2647, 2719, 2767, 2791, 3079, 3319, 3343, 3511, 3559, 3583, 3607, 3823, 3847, 3967, 4111, 4231, 4567, 4639, 4663
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Discriminant=-1056. Also primes of the form 7x^2+4xy+76y^2.
In base 12, the sequence is 7, 67, X7, 107, 1X7, 307, 427, 647, 687, 747, 867, 927, 987, X07, X27, E67, 1027, 11X7, 1367, 13X7, 1467, 1547, 1587, 1647, 16X7, 1727, 1747, 1947, 1E07, 1E27, 2047, 2087, 20X7, 2107, 2267, 2287, 2367, 2467, 2547, 2787, 2827, 2847, 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), Jun 01 2008
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MATHEMATICA
| Union[QuadPrimes[7, 6, 39, 10000], QuadPrimes[7, -6, 39, 10000]] (* see A106856 *)
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CROSSREFS
| Cf. A140633.
Sequence in context: A106107 A020471 A065902 * A139945 A023285 A135051
Adjacent sequences: A140610 A140611 A140612 * A140614 A140615 A140616
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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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