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A024407
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Areas of more than one primitive Pythagorean triangle.
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7
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210, 2730, 7980, 71610, 85470, 106260, 114114, 234780, 341880, 420420, 499590, 1563660, 1647030, 1857240, 2042040, 3423420, 3666390, 6587490, 7393470, 8514660, 9279270, 12766110, 13123110, 17957940, 18820830, 23393370, 23573550, 29099070, 29274630, 29609580
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OFFSET
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1,1
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COMMENTS
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Among a(1) to a(30), only a(23) = 13123110 has multiplicity 3, the others have multiplicity 2. The three primitive Pythagorean triangles corresponding to a(23) are [4485, 5852, 7373], [3059, 8580, 9109] and [19019, 1380, 19069]. Leg exchange is not taken into account. - Wolfdieter Lang, Jun 15 2015
The area 13123110 of multiplicity three was discovered by C. L. Shedd in 1945, cf. Beiler, Gardner and Weisstein. - M. F. Hasler, Jan 20 2019
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REFERENCES
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A. H. Beiler: The Eternal Triangle. Ch. 14 in Recreations in the Theory of Numbers: The Queen of Mathematics Entertains. Dover, 1966, p. 127.
M. Gardner: The Sixth Book of Mathematical Games from Scientific American. University of Chicago Press, 1984, pp. 160-161.
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LINKS
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FORMULA
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EXAMPLE
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The first repeated terms in A024406 are:
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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