

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



FORMULA



EXAMPLE

The first repeated terms in A024406 are:


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



