A081962 Ordered semiperimeters of primitive Pythagorean triangles with an even short leg (or an odd long leg).

20, 35, 42, 63, 72, 88, 99, 110, 130, 143, 156, 165, 195, 210, 221, 238, 255, 266, 272, 285, 304, 323, 336, 342, 357, 391, 399, 414, 420, 437, 450, 460, 475, 483, 506, 525, 540, 550, 575, 594, 600, 609, 621, 638, 667, 675, 682, 696, 702, 713, 725, 744, 754

Offset

1,1

Comments

If m and n are the generators of the primitive Pythagorean triples (PPT) with m>n, GCD(m,n)=1 and (m+n) odd then the odd leg is m^2-n^2 and the even leg is 2m*n. Therefore the even leg is shortest if 2m*n<m^2-n^2, i.e., m>(1+sqrt(2))*n. Also this is a sequence of numbers whose square is the semiperimeter of a PPT. - Frank M Jackson, Oct 10 2014

Links

Ray Chandler, Table of n, a(n) for n = 1..10000 (first 1621 terms from Vincenzo Librandi)

Mathematica

lst1 = {}; Do[If[GCD[m, n]==1&&m(Sqrt[2]+1)<n&&OddQ[m+n], AppendTo[lst1, n(m+n)]],  {n, 1, 100}, {m, 1, n}]; Sort@lst1 (* Frank M Jackson, Oct 10 2014 *)

Crossrefs

Sequence in context: A325603 A024747 A328051 * A024755 A048022 A255349

Adjacent sequences: A081959 A081960 A081961 * A081963 A081964 A081965

Keyword

nonn

Author

Lekraj Beedassy, Apr 23 2003

Extensions

More terms from Ray Chandler, Oct 29 2003

Status

approved