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Search: id:A140629
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| A140629 |
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Primes of the form 76x^2+20xy+145y^2. |
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+0
1
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| 241, 409, 769, 1321, 1489, 2281, 3001, 4129, 4441, 5449, 5689, 6121, 6481, 6961, 7129, 7321, 7369, 8209, 9001, 11161, 11329, 11689, 12241, 12409, 13249, 13681, 13921, 14929, 15361, 16369, 16729, 17041, 17401, 17569, 17881, 18049, 18289
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Discriminant=-43680. Also primes of the form 96x^2+72xy+241y^2.
In base 12, the sequence is 181, 2X1, 541, 921, X41, 13X1, 18X1, 2481, 26X1, 31X1, 3361, 3661, 3901, 4041, 4161, 42X1, 4321, 4901, 5261, 6561, 6681, 6921, 7101, 7221, 7801, 7E01, 8081, 8781, 8X81, 9581, 9821, 9X41, X0X1, X201, X421, X541, X701, where X is 10 and E is 11. Moreover, the discriminant is -21340. 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
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Union[QuadPrimes[76, 20, 145, 10000], QuadPrimes[76, -20, 145, 10000]] (* see A106856 *)
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CROSSREFS
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Cf. A140633.
Sequence in context: A050968 A142918 A139502 this_sequence A137771 A108831 A068706
Adjacent sequences: A140626 A140627 A140628 this_sequence A140630 A140631 A140632
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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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