A297878 1/4 of the even edges of primitive Pythagorean triangles with legs (b=A081872, c=A081859), ordered by semiperimeters.

1, 3, 2, 6, 5, 3, 10, 7, 15, 4, 14, 12, 21, 9, 20, 5, 18, 28, 15, 11, 36, 6, 22, 35, 33, 45, 13, 30, 44, 7, 26, 42, 55, 21, 39, 15, 35, 8, 52, 66, 30, 65, 24, 63, 17, 78, 40, 9, 60, 77, 34, 56, 91, 51, 19, 72, 45, 10, 68, 88, 105, 38, 63, 85, 30, 104, 57, 21, 102, 120, 11, 76, 99, 42, 119, 70, 33, 95

Offset

1,2

Comments

It seems that all positive integers are included.

Every term has the form of edge length e = (v-u)*u/2, semiperimeter s = (h+b+c)/2 = u*v with b > c, h^2 = b^2 + c^2, u < v < 2*u, v odd (see Theorem 3 of Witcosky).

Links

Table of n, a(n) for n=1..78.

Wikipedia, Pythagorean triple.

Lindsey Witcosky, Perimeters of primitive Pythagorean triangles.

Index entries related to Pythagorean Triples.

Example

From Michel Marcus, Mar 07 2018: (Start)
The first 10 terms of A081859 are 3,  5,  8,  7, 20, 12,  9, 28, 11, 16;
The first 10 terms of A081872 are 4, 12, 15, 24, 21, 35, 40, 45, 60, 63;
So the first 10 even legs are     4, 12,  8, 24, 20, 12, 40, 28, 60, 16;
So the first 10 terms are         1,  3,  2,  6,  5,  3, 10,  7, 15,  4. (End)

Mathematica

(* lists a0* have to be prepared before *)
opPT = {a020882, a046087, a046086, a020882 + a046087 + a046086} topPT = Transpose[opPT]; stopPT = SortBy[topPT, {#[[4]]} &]; tstopPT = Transpose[stopPT]; nopPT = tstopPT; Do[ If[OddQ[tstopPT[[2]][[k]]], nopPT[[2]][[k]] = tstopPT[[2]][[k]]; nopPT[[3]][[k]] = tstopPT[[3]][[k]], nopPT[[2]][[k]] = tstopPT[[3]][[k]]; nopPT[[3]][[k]] = tstopPT[[2]][[k]]], {k, 1, 10000}]; nopPT[[3]]/4

Crossrefs

Cf. A298042((odd edge - 1)/2), A081872(b), A081859(c).

Cf. A231100 (even legs ordered by hypotenuse).

Sequence in context: A090571 A088452 A268719 * A234922 A049777 A193999

Adjacent sequences: A297875 A297876 A297877 * A297879 A297880 A297881

Keyword

nonn

Author

Ralf Steiner, Jan 07 2018

Status

approved