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Search: id:A121992
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| A121992 |
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Eisenstein triples : {a,b,c} such {a^2+b^2-a*b-c^2=0}and Abs[a-b]>0 sorted by greatest a. |
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1
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| 3, 8, 7, 5, 8, 7, 5, 21, 19, 6, 16, 14, 7, 15, 13, 8, 3, 7, 8, 5, 7, 8, 15, 13, 9, 24, 21, 10, 16, 14, 15, 7, 13, 15, 8, 13, 15, 24, 21, 16, 6, 14, 16, 10, 14, 16, 21, 19, 21, 5, 19, 21, 16, 19, 24, 9, 21, 24, 15, 21
(list; graph; listen)
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OFFSET
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1,1
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REFERENCES
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Ross Honsberger, "Mathematical Delights", MAA, 2004, p. 64.
A similar factoring allows for the generation of Eisenstein triples, which are numbers. which form the sides of a triangle with a 60-degree angle: http://mathforum.org/pcmi/hstp/sum2001/wg/number.theory/session13.pdf#search=%22Eisenstein%20triples%22
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FORMULA
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T(n) = {a[n],b[n],c[n]} such that a[n]^2+b[n]^2-a[n]*b[n]-c[n]^2=0 and Abs[a[n]-b[n]]>0
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EXAMPLE
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Grouped as threes:
{{3, 8, 7}, {5, 8, 7}, {5, 21, 19}, {6, 16, 14}, {7, 15, 13}, {8, 3, 7}, {8, 5, 7}, {8, 15, 13}, {9, 24, 21}, {10, 16, 14}, {15, 7, 13}, {15, 8, 13}, {15, 24, 21}, {16,6, 14}, {16, 10, 14}, {16, 21, 19}, {21, 5, 19}, {21, 16, 19}, {24, 9, 21}, {24, 15, 21}}
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MATHEMATICA
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f[a_, b_, c_] = If[c^2 - a^2 - b^2 + a*b == 0 && Abs[a - b] > 0, {a, b, c}, {}] a0 = Flatten[Delete[Union[Table[Delete[Union[Table[Flatten[Table[f[a, b, c], {c, 1, 25}]], {b, 1, 25}]], 1], {a, 1, 25}]], 1], 1] b0 = Sort[a0] Flatten[b0]
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CROSSREFS
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Cf. A046063.
Sequence in context: A016671 A010472 A134903 this_sequence A021262 A153020 A106043
Adjacent sequences: A121989 A121990 A121991 this_sequence A121993 A121994 A121995
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KEYWORD
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nonn,uned
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AUTHOR
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Roger Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Sep 10 2006
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