A298042 (d-1)/2 of the odd edges d of primitive Pythagorean triangles with legs (b=A081872, c=A081859), ordered by semiperimeters.

1, 2, 7, 3, 10, 17, 4, 22, 5, 31, 16, 27, 6, 38, 19, 49, 32, 7, 45, 58, 8, 71, 52, 25, 42, 9, 82, 59, 28, 97, 76, 47, 10, 93, 66, 110, 85, 127, 52, 11, 104, 34, 123, 57, 142, 12, 115, 161, 80, 37, 136, 103, 13, 126, 178, 87, 149, 199, 112, 67, 14, 172, 137, 94, 195, 43, 162, 218, 72, 15, 241

Offset

1,2

Comments

It seems that all positive integers are included.

Every term is equal to (d-1)/2 with d = 2*u*v - v^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..71.

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 odd legs are      3,  5, 15,  7, 21, 35,  9, 45, 11, 63;
So the first 10 terms are         1,  2,  7,  3, 10, 17,  4, 22,  5, 31. (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[[2]] - 1)/2

Crossrefs

Cf. A297878 (even edge /4), A081872(b), A081859(c).

Cf. A180620 (odd legs sorted on hypotenuse).

Sequence in context: A227415 A361207 A309156 * A051430 A185510 A304754

Adjacent sequences: A298039 A298040 A298041 * A298043 A298044 A298045

Keyword

nonn

Author

Ralf Steiner, Jan 11 2018

Status

approved