

A253803


a(n) gives one fourth of the even leg of one of the two Pythagorean triangles with hypotenuse A080109(n) = A002144(n)^2. The odd leg is given in A253802(n).


3



6, 39, 60, 210, 210, 410, 630, 915, 1320, 1780, 2340, 990, 2730, 3164, 4620, 5215, 5610, 4290, 8145, 8106, 2730, 6630, 12116, 12540, 4080, 17485, 17451, 18480, 9690, 24414
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OFFSET

1,1


COMMENTS

See A253802 for comments and the Dickson reference.


REFERENCES

L. E. Dickson, History of the Theory of Numbers, Carnegie Institution, Publ. No. 256, Vol. II, Washington D.C., 1920, p. 227.


LINKS

Table of n, a(n) for n=1..30.


FORMULA

a(n) = sqrt(A080109(n)^2  A253802(n)^2)/4, n >= 1.


EXAMPLE

n = 7: A080175(7) = 7890481 = 53^4 = 2809^2; A002144(7)^4 = A253802(7)^2 + (4*a(7))^2 = 1241^2 + (4*630)^2.
The other Pythagorean triangle with hypotenuse
53^2 = 2809 has odd leg A253804(7) = 2385 and even leg 4*A253305(7) = 4*371 = 1484: 53^4 = 2385^2 + (4*371)^2.


CROSSREFS

Cf. A002144, A080109, A253802, A253804, A253805.
Sequence in context: A241258 A061423 A080298 * A058897 A058985 A116951
Adjacent sequences: A253800 A253801 A253802 * A253804 A253805 A253806


KEYWORD

nonn,easy


AUTHOR

Wolfdieter Lang, Jan 14 2015


STATUS

approved



