A055193 Smallest number that is the area of n distinct Pythagorean triangles.

6, 210, 840, 341880, 71831760, 64648584000, 2216650756320, 22861058133513600

Offset

1,1

Comments

a(9) <= 14456267383718160000 the triangles are 3188885700-9066657600-9611101500, 8199991800-3525922400-8925917000, 2333331000-12391098720-12608876280, 29569667400-977776800-29585829000, 11569432875-2499045120-11836258005, 2179485000-13265764512-13443610488, 8493324840-3404148000-9150125160, 1027776750-28131143040-28149911790, 313939080-92096004000-92096539080. - Felipe Villaseñor, Oct 29 2024

Links

Table of n, a(n) for n=1..8.

Example

a(5) = 71831760 is area of 5 Pythagorean triangles: 2415-59488-59537, 2640-54418-54482, 5070-28336-28786, 7280-19734-21034, 10010-14352-17498
From Sture Sjöstedt, Jun 09 2017: (Start)
The area of 7280-19734-21034 is (2*13)^2*the area of 280-759-809.
The area of 10010-14352-17498 is (2*13)^2*the area of 385-552-673.
These triangles have the same area as the triangles I get by solving p^2-p*q+q^2=r^2. r=169, p=15, q=176, (q-p)=161 Area=r*p*q*(q-p)
q=176 and r=169 gives 2415-59488-59537;
r=169 and q-p=161 gives 2640-54418-54482;
r=169 and p=15 gives 5070-28336-28786. (End)

Crossrefs

Cf. A009111, A093536.

Sequence in context: A068969 A335715 A094805 * A346015 A001505 A327248

Adjacent sequences: A055190 A055191 A055192 * A055194 A055195 A055196

Keyword

nonn,more

Author

David W. Wilson, Jun 30 2000

Extensions

Edited by N. J. A. Sloane, Sep 15 2008 at the suggestion of R. J. Mathar

a(8) added by Duncan Moore, Mar 10 2017

Status

approved