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Search: id:A139508
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| A139508 |
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Primes of the form x^2 + 28x*y + y^2 for x and y nonnegative. |
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2
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| 61, 181, 601, 829, 1069, 1249, 1381, 1429, 1609, 1621, 1741, 2029, 2089, 2161, 2341, 2389, 2521, 3121, 3169, 3181, 3301, 3709, 3769, 4021, 4261, 4549, 4729, 4801, 4861, 4969, 5209, 5281, 5521, 5581, 5641, 5749, 5821, 6301, 6361, 6421, 6529, 6709, 6829
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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In base 12, the sequence is 51, 131, 421, 591, 751, 881, 971, 9E1, E21, E31, 1011, 1211, 1261, 1301, 1431, 1471, 1561, 1981, 1X01, 1X11, 1XE1, 2191, 2221, 23E1, 2571, 2771, 28X1, 2941, 2991, 2X61, 3021, 3081, 3241, 3291, 3321, 33E1, 3451, 3791, 3821, 3871, 3941, 3X71, 3E51, where X is 10 and E is 11. Moreover, the discriminant is 550. 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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a = {}; w = 28; k = 1; Do[Do[If[PrimeQ[n^2 + w*n*m + k*m^2], AppendTo[a, n^2 + w*n*m + k*m^2]], {n, m, 400}], {m, 1, 400}]; Union[a] (*Artur Jasinski*)
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CROSSREFS
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Cf. A139489, A007645, A068228, A007519, A033212, A033212, A107152, A107008, A033215, A107145, A139490, A139491.
Sequence in context: A088955 A087870 A121513 this_sequence A087871 A038643 A142267
Adjacent sequences: A139505 A139506 A139507 this_sequence A139509 A139510 A139511
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KEYWORD
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nonn
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AUTHOR
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Artur Jasinski (grafix(AT)csl.pl), Apr 24 2008
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