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A024407 Areas of more than one primitive Pythagorean triangle. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

REFERENCES

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.

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..200

Ron Knott, Pythagorean Triples and Online Calculators

Eric W. Weisstein, Primitive Right Triangle, on MathWorld.Wolfram.com.

FORMULA

Terms occuring more than once in A024406 listed exactly once: { n = A024406(k): n = A024406(k+m), m > 0 }. - M. F. Hasler, Jan 20 2019, edited by David A. Corneth, Jan 21 2019

EXAMPLE

The first repeated terms in A024406 are:

   A024406(6) = A024406(7) = 210 = a(1),

   A024406(24) = A024406(25) = 2730 = a(2),

   A024406(42) = A024406(43) = 7980 = a(3). - M. F. Hasler, Jan 20 2019

CROSSREFS

Cf. A024365, A024406.

Sequence in context: A187663 A064260 A027806 * A027822 A024449 A235240

Adjacent sequences:  A024404 A024405 A024406 * A024408 A024409 A024410

KEYWORD

nonn

AUTHOR

David W. Wilson

EXTENSIONS

a(29) and a(30) added by Wolfdieter Lang, Jun 14 2015

STATUS

approved

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Last modified June 18 17:05 EDT 2019. Contains 324214 sequences. (Running on oeis4.)