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Search: id:A024365
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| A024365 |
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Areas of right triangles with co-prime integer sides. |
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+0
7
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| 6, 30, 60, 84, 180, 210, 330, 504, 546, 630, 840, 924, 990, 1224, 1320, 1386, 1560, 1710, 1716, 2310, 2340, 2574, 2730, 3036, 3570, 3900, 4080, 4290, 4620, 4914, 5016, 5610, 5814, 6090, 6630, 7140, 7440, 7854, 7956, 7980, 8970, 8976, 9690, 10374
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Consider primitive Pythagorean triangles (A^2 + B^2 = C^2, (A, B) = 1, A <= B); sequence gives areas A*B/2.
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FORMULA
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Positive integers of the form u*v*(u^2-v^2) where 2uv and u^2-v^2 are co-prime or, alternatively, where u,v are co-prime and one of them is even.
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EXAMPLE
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6 is in the sequence because it is the area of the 3-4-5 triangle is the integer 6.
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CROSSREFS
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Cf. A009111, A009112.
Subsequence of A073120 and A147778.
Sequence in context: A014203 A044083 A024406 this_sequence A057229 A120734 A116360
Adjacent sequences: A024362 A024363 A024364 this_sequence A024366 A024367 A024368
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KEYWORD
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nonn
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net)
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EXTENSIONS
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Additional comments James Buddenhagen (jbuddenh(AT)gmail.com), Aug 10 2008 and from Max Alekseyev, Nov 12 2008
Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 20 2008 at the suggestion of R. J. Mathar
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