A024407 - OEIS

%I #38 Jul 22 2020 11:31:42

%S 210,2730,7980,71610,85470,106260,114114,234780,341880,420420,499590,

%T 1563660,1647030,1857240,2042040,3423420,3666390,6587490,7393470,

%U 8514660,9279270,12766110,13123110,17957940,18820830,23393370,23573550,29099070,29274630,29609580

%N Areas of more than one primitive Pythagorean triangle.

%C 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

%C 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

%D A. H. Beiler: The Eternal Triangle. Ch. 14 in Recreations in the Theory of Numbers: The Queen of Mathematics Entertains. Dover, 1966, p. 127.

%D M. Gardner: The Sixth Book of Mathematical Games from Scientific American. University of Chicago Press, 1984, pp. 160-161.

%H Giovanni Resta, <a href="/A024407/b024407.txt">Table of n, a(n) for n = 1..200</a>

%H Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Pythag/pythag.html">Pythagorean Triples and Online Calculators</a>

%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/PrimitiveRightTriangle.html">Primitive Right Triangle</a>, on MathWorld.Wolfram.com.

%F 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

%e The first repeated terms in A024406 are:

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

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

%e    A024406(42) = A024406(43) = 7980 = a(3). - _M. F. Hasler_, Jan 20 2019

%Y Cf. A024365, A024406.

%K nonn

%O 1,1

%A _David W. Wilson_

%E a(29) and a(30) added by _Wolfdieter Lang_, Jun 14 2015