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Search: id:A140616
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| A140616 |
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Primes of the form 5x^2+4xy+68y^2. |
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+0
2
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| 5, 101, 173, 269, 293, 461, 509, 677, 773, 797, 941, 1013, 1109, 1181, 1277, 1301, 1613, 1637, 1949, 1973, 2141, 2309, 2357, 2477, 2621, 2693, 2789, 2861, 2957, 3461, 3533, 3701, 3797, 3821, 3989, 4133, 4157, 4373, 4493, 4637, 4877, 4973
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Discriminant=-1344. Also primes of the form 5x^2+2xy+101y^2.
In base 12, the sequence is 5, 85, 125, 1X5, 205, 325, 365, 485, 545, 565, 665, 705, 785, 825, 8X5, 905, E25, E45, 1165, 1185, 12X5, 1405, 1445, 1525, 1625, 1685, 1745, 17X5, 1865, 2005, 2065, 2185, 2245, 2265, 2385, 2485, 24X5, 2645, 2725, 2825, 29X5, 2X65, where X is for 10 and E is for 11. Moreover, the discriminant is -940. 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[5, 4, 68, 10000], QuadPrimes[5, -4, 68, 10000]] (* see A106856 *)
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CROSSREFS
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Cf. A140633.
Sequence in context: A141120 A123668 A090436 this_sequence A087456 A081220 A041187
Adjacent sequences: A140613 A140614 A140615 this_sequence A140617 A140618 A140619
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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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