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Search: id:A140624
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| A140624 |
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Primes of the form 19x^2+14xy+91y^2. |
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| 19, 139, 619, 691, 811, 859, 1291, 1459, 1531, 1699, 2131, 2371, 2539, 2659, 2971, 3331, 3499, 4051, 4219, 4339, 4651, 5011, 5059, 5179, 5659, 5851, 6571, 6691, 7411, 7699, 8011, 8179, 8419, 8539, 9091, 9859, 9931, 10099, 10531, 10771, 10891
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OFFSET
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1,1
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COMMENT
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Discriminant=-6720. Also primes of the form 19x^2+16xy+136y^2.
In base 12, the sequence is 17, E7, 437, 497, 577, 5E7, 8E7, X17, X77, E97, 1297, 1457, 1577, 1657, 1877, 1E17, 2037, 2417, 2537, 2617, 2837, 2X97, 2E17, 2EE7, 3337, 3477, 3977, 3X57, 4357, 4557, 4777, 4897, 4X57, 4E37, 5317, 5857, 58E7, 5X17, 6117, 6297, 6377, where X is 10 and E is 11. Moreover, the discriminant is -3X80. 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[19, 14, 91, 10000], QuadPrimes[19, -14, 91, 10000]] (* see A106856 *)
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CROSSREFS
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Cf. A140633.
Sequence in context: A101090 A142746 A139902 this_sequence A057636 A104046 A060104
Adjacent sequences: A140621 A140622 A140623 this_sequence A140625 A140626 A140627
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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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