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A088977
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Side of primitive equilateral triangle with prime cevian p=A002476(n) cutting an edge into two integral parts.
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7
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8, 15, 21, 35, 40, 48, 65, 77, 80, 91, 112, 117, 119, 133, 160, 168, 171, 187, 207, 209, 221, 224, 253, 255, 264, 280, 312, 323, 325, 341, 352, 377, 391, 403, 408, 425, 435, 440, 455, 465, 483, 504, 525, 527, 560, 576, 595, 609, 624, 645, 651, 665, 667, 703
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The edge a(n) is partitioned into q=s^2 - t^2=A088243(n)*A088296(n) and r=t(2s+t)=A088242(n)*A088299(n) by a cevian of length p. [Alternatively, (p,q,r) form a triangle with angle 2pi/3 opposite side p.] The quadruple {p,q,r,a(n)=q+r} satisfies the triangle relation: see A061281, or the simpler relation a(n)^2 = p^2 + q*r.
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LINKS
| F. Barnes, Deriving 60 degree triples
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FORMULA
| a(n) = A088241(n)*A088298(n) = s(s+2t), where s^2 + st + t^2, with s>t, form the primes p = 1 (mod 6) = A002476(n).
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CROSSREFS
| Cf. A002476, A088241, A088242, A088243, A088296, A088298, A088299.
Sequence in context: A082867 A075713 A089025 * A070043 A003786 A008686
Adjacent sequences: A088974 A088975 A088976 * A088978 A088979 A088980
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KEYWORD
| nonn
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AUTHOR
| Lekraj Beedassy (blekraj(AT)yahoo.com), Oct 31 2003
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EXTENSIONS
| More terms from Ray Chandler (rayjchandler(AT)sbcglobal.net), Nov 01 2003
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