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Search: id:A139506
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| A139506 |
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Primes of the form x^2 + 26x*y + y^2 for x and y nonnegative. |
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4
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| 193, 337, 457, 673, 1009, 1033, 1129, 1201, 1297, 1801, 1873, 2017, 2137, 2377, 2473, 2521, 2689, 2713, 2857, 3049, 3217, 3313, 3361, 3529, 3697, 3889, 4057, 4153, 4201, 4561, 4657, 4729, 4993, 5209, 5233, 5569, 5737, 5881, 6073, 6217, 6337, 6553, 6577
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Also primes of the form x^2 + 168y^2. - T. D. Noe (noe(AT)sspectra.com), Apr 29 2008
In base 12, the sequence is 141, 241, 321, 481, 701, 721, 7X1, 841, 901, 1061, 1101, 1201, 12X1, 1461, 1521, 1561, 1681, 16X1, 17X1, 1921, 1X41, 1E01, 1E41, 2061, 2181, 2301, 2421, 24X1, 2521, 2781, 2841, 28X1, 2X81, 3021, 3041, 3281, 33X1, 34X1, 3621, 3721, 3801, 3961, 3981, where X is 10 and E is 11. Moreover, the discriminant is 480. 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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FORMULA
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The primes are congruent to {1, 25, 121} (mod 168). - T. D. Noe (noe(AT)sspectra.com), Apr 29 2008
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MATHEMATICA
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a = {}; w = 26; 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.
Cf. A139643.
Sequence in context: A015988 A142743 A014755 this_sequence A147171 A146824 A142453
Adjacent sequences: A139503 A139504 A139505 this_sequence A139507 A139508 A139509
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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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