A024407 Areas of more than one primitive Pythagorean triangle.

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

Offset: 1

Author

David W. Wilson

Keywords

• nonn

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

Examples

			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
		

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.

Crossrefs

Cf. A024365, A024406.

Formula

Terms occurring 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

Extensions

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