

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. 160161.


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



