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Search: id:A140617
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| A140617 |
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Primes of the form 11x^2+8xy+32y^2. |
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| 11, 107, 179, 347, 443, 491, 659, 683, 827, 947, 1019, 1163, 1187, 1283, 1451, 1499, 1523, 1619, 1667, 1787, 2003, 2027, 2339, 2459, 2531, 2699, 2843, 2963, 3011, 3203, 3299, 3347, 3371, 3467, 3539, 3803, 3851, 4019, 4139, 4211, 4523, 4547
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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 11x^2+4xy+92y^2.
In base 12, the sequence is E, 8E, 12E, 24E, 30E, 34E, 46E, 48E, 58E, 66E, 70E, 80E, 82E, 8XE, X0E, X4E, X6E, E2E, E6E, 104E, 11XE, 120E, 142E, 150E, 156E, 168E, 178E, 186E, 18XE, 1X2E, 1XXE, 1E2E, 1E4E, 200E, 206E, 224E, 228E, 23XE, 248E, 252E, 274E, 276E, 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[11, 8, 32, 10000], QuadPrimes[11, -8, 32, 10000]] (* see A106856 *)
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CROSSREFS
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Cf. A140633.
Sequence in context: A075183 A116011 A058715 this_sequence A163413 A001721 A080158
Adjacent sequences: A140614 A140615 A140616 this_sequence A140618 A140619 A140620
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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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