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A268602 Numerator of the side lengths (legs in ascending order) of the easiest Pythagorean Triangle (with smallest hypotenuse) according to the congruent numbers A003273. 1
3, 20, 41, 3, 4, 5, 35, 24, 337, 780, 323, 106921, 8, 63, 65, 4, 15, 17, 3, 40, 41, 7, 12, 25, 33, 140, 4901, 80155, 41496, 905141617 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Every three fractions x < y < z satisfy the Pythagorean equation x^2 + y^2 = z^2: (a(3*n-2)/A268603(3*n-2))^2 + (a(3*n-1)/A268603(3*n-1))^2 = (a(3*n)/A268603(3*n))^2.

The area A = x*y/2 of these Pythagorean triangles is a congruent number: A003273(n) = (1/2) * a(3*n-2)/A268603(3*n-2) * a(3*n-1)/A268603(3*n-1)).

LINKS

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

Eric Weisstein's World of Mathematics, Congruent Number.

EXAMPLE

The first congruent number is 5 and the associated right triangle with the side lengths x = 3/2, y = 20/3, z = 41/6 satisfies the Pythagorean equation (3/2)^2 + (20/3)^2 = (41/6)^2 and the area of this triangle equals 1/2*3/2*20/3 = 5.

CROSSREFS

Cf. A003273, A268603.

Sequence in context: A254501 A031106 A248818 * A267055 A296252 A211068

Adjacent sequences:  A268599 A268600 A268601 * A268603 A268604 A268605

KEYWORD

nonn,frac,more,tabf

AUTHOR

Martin Renner, Feb 08 2016

STATUS

approved

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Last modified December 16 04:05 EST 2019. Contains 330013 sequences. (Running on oeis4.)