A226485 Integer part of length of median to hypotenuse of primitive Pythagorean triangles sorted on hypotenuse.

2, 6, 8, 12, 14, 18, 20, 26, 30, 32, 32, 36, 42, 42, 44, 48, 50, 54, 56, 62, 68, 72, 72, 74, 78, 84, 86, 90, 92, 92, 96, 98, 102, 102, 110, 110, 114, 116, 120, 128, 132, 132, 134, 138, 140, 144, 146, 152, 152, 156, 158, 162, 162, 168, 174, 176, 182, 182

Offset

1,1

Comments

The median to hypotenuse is equal to the circumradius.

The length of the median is sqrt((a^2)/2 + (b^2)/2 - (c^2)/4) where a,b,c are sides of the triangle. In case of Pythagorean triangles, m=h/2 were h is the hypotenuse.

Links

Table of n, a(n) for n=1..58.

Ron Knott, Pythagorean Triples and Online Calculators

Formula

a(n) = floor(A020882(n)/2).

Example

a(1)=2 as it is the integer portion of the length of the median to hypotenuse of triangle having sides 3,4,5.
Similarly, a(5)=14 as it is the integer portion of the length of the median to hypotenuse of triangle having sides 20,21,29.

Crossrefs

Cf. A020882.

Sequence in context: A189933 A229488 A307699 * A213638 A191965 A173064

Adjacent sequences: A226482 A226483 A226484 * A226486 A226487 A226488

Keyword

nonn

Author

Mihir Mathur, Jun 09 2013

Status

approved