A055193 - OEIS

%I #44 Nov 01 2024 03:45:43

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

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

%C 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

%e a(5) = 71831760 is area of 5 Pythagorean triangles: 2415-59488-59537, 2640-54418-54482, 5070-28336-28786, 7280-19734-21034, 10010-14352-17498

%e From _Sture Sjöstedt_, Jun 09 2017: (Start)

%e The area of 7280-19734-21034 is (2*13)^2*the area of 280-759-809.

%e The area of 10010-14352-17498 is (2*13)^2*the area of 385-552-673.

%e 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)

%e q=176 and r=169 gives 2415-59488-59537;

%e r=169 and q-p=161 gives 2640-54418-54482;

%e r=169 and p=15 gives 5070-28336-28786. (End)

%Y Cf. A009111, A093536.

%K nonn,more

%O 1,1

%A _David W. Wilson_, Jun 30 2000

%E Edited by _N. J. A. Sloane_, Sep 15 2008 at the suggestion of _R. J. Mathar_

%E a(8) added by _Duncan Moore_, Mar 10 2017