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Search: id:A139490
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| A139490 |
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Numbers n such that the quadratic form x^2 + n*x*y + y^2 represents exactly the same primes as the quadratic form x^2 + m*y^2 for some m. |
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+0
23
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| 1, 4, 6, 7, 8, 10, 14, 16, 18, 22, 26, 38
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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It may be that there are no further terms?
For the numbers m see A139491
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EXAMPLE
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a(1)=1 because the primes represented bny x^2+xy+y^2 are the same as the primes represented by x^2 + 3*y^2 (see A007645).
The known pairs (n,m) are the following (checked for range n<=200 and m<=500):
n={1, 4, 4, 6, 6, 7, 8, 8, 10, 10, 10, 14, 14, 14, 16, 18, 22, 22, 26, 38, 38}
m={3, 9, 12, 8, 16, 15, 45, 60, 24, 48, 72, 24, 48, 72, 21, 40, 120, 240, 168, 120, 240}
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MATHEMATICA
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Timing[f = 200; g = 300; h = 30; j = 100; b = {}; Do[a = {}; Do[Do[If[PrimeQ[x^2 + n y^2], AppendTo[a, x^2 + n y^2]], {x, 0, g}], {y, 1, g}]; AppendTo[b, Take[Union[a], h]], {n, 1, f}]; Print[b]; c = {}; Do[a = {}; Do[Do[If[PrimeQ[n^2 + w*n*m + m^2], AppendTo[a, n^2 + w*n*m + m^2]], {n, m, g}], {m, 1, g}]; AppendTo[c, Take[Union[a], h]], {w, 1, j}]; Print[c]; bb = {}; cc = {}; Do[Do[If[b[[p]] == c[[q]], AppendTo[bb, p]; AppendTo[cc, q]], {p, 1, f}], {q, 1, j}]; Union[cc]] (*Artur Jasinski*)
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CROSSREFS
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Cf. A139489, A007645, A068228, A007519, A033212, A033212, A107152, A107008, A033215, A107145.
Adjacent sequences: A139487 A139488 A139489 this_sequence A139491 A139492 A139493
Sequence in context: A079000 A047509 A105432 this_sequence A030375 A081712 A084395
Cf. A139491.
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KEYWORD
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nonn,new
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AUTHOR
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Artur Jasinski (grafix(AT)csl.pl), Apr 24 2008, Apr 26 2008, Apr 27 2008
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EXTENSIONS
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Edited by njas, Apr 25 2008
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