A253805 a(n) gives one fourth of the even leg of the second of the two Pythagorean triangles with hypotenuse A080109(n) = A002144(n)^2. The odd leg is given in A253804.

5, 30, 34, 145, 111, 180, 371, 330, 876, 1560, 1746, 505, 1635, 840, 3014, 3570, 5181, 2249, 1710, 7980, 1379, 3435, 10920, 7230, 2056, 8970, 14490, 11240, 4981, 3900

Offset

1,1

Comments

See A253804 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 - A253804(n)^2)/4, n >= 1.

Example

n = 7: A080175(7) = 7890481 = 53^4 = 2809^2; A002144(7)^4 = A253804(7)^2 + (4*a(7))^2 = 2385^2 + (4*371)^2.
The other Pythagorean triangle with hypotenuse 53^2 = 2809 has odd leg A253802(7) = 1241 and even leg 4*A253303(7) = 4*630 = 2520: 53^4 = 1241^2 + (4*630)^2.

Crossrefs

Cf. A002144, A080109, A253804, A253802, A253803.

Sequence in context: A098346 A134166 A154522 * A222463 A097252 A169610

Adjacent sequences: A253802 A253803 A253804 * A253806 A253807 A253808

Keyword

nonn,easy

Author

Wolfdieter Lang, Jan 16 2015

Status

approved