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A298042 (d-1)/2 of the odd edges d of primitive Pythagorean triangles with legs (b=A081872, c=A081859), ordered by semiperimeters. 1
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 (list; graph; refs; listen; history; text; internal format)
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 to sequences related to Pythagorean triples

EXAMPLE

From Michel Marcus, Mar 07 2018: (Start)

The 10 first terms of A081859 are 3,  5,  8,  7, 20, 12,  9, 28, 11, 16;

The 10 first terms of A081872 are 4, 12, 15, 24, 21, 35, 40, 45, 60, 63;

So the 10 first odd legs are      3,  5, 15,  7, 21, 35,  9, 45, 11, 63;

So the 10 first 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: A021369 A242304 A227415 * A051430 A185510 A304754

Adjacent sequences:  A298039 A298040 A298041 * A298043 A298044 A298045

KEYWORD

nonn

AUTHOR

Ralf Steiner, Jan 11 2018

STATUS

approved

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Last modified January 15 19:06 EST 2019. Contains 319171 sequences. (Running on oeis4.)