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A201223
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Primitive Eisenstein triples (a,b,c) listed as groups of three in order of increasing b.
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4
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3, 8, 7, 5, 8, 7, 7, 15, 13, 8, 15, 13, 5, 21, 19, 16, 21, 19, 11, 35, 31, 24, 35, 31, 7, 40, 37, 33, 40, 37, 13, 48, 43, 35, 48, 43, 16, 55, 49, 39, 55, 49, 9, 65, 61, 56, 65, 61, 32, 77, 67, 45, 77, 67, 17, 80, 73, 63, 80, 73, 40, 91, 79, 51, 91, 79, 11, 96, 91
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OFFSET
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1,1
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COMMENTS
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An Eisenstein triple is a triple (a,b,c) of positive integers with a<c<b and a^2 - a*b + b^2 = c^2. It is primitive if a, b, and c are relatively prime.
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LINKS
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EXAMPLE
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(a,b,c)=(3,8,7) is an Eisenstein triple since 3<7<8 and 3^2 - 3*8 + 8^2 = 7^2. GCD(3,8,7) = 1, so the triple is primitive. No Eisenstein triple exists with b<8, so a(1)=3, a(2)=8, a(3)=7.
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MATHEMATICA
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x = {}; For[b = 1, b <= 77, b++, For[c = 1, c < b, c++, For[a = 1, a < c, a++, {If[(a^2 - a*b + b^2 == c^2) && (GCD[a, b, c] == 1), AppendTo[x, {a, b, c}]]}]]]; Flatten[x]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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