

A298042


(d1)/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
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OFFSET

1,2


COMMENTS

It seems that all positive integers are included.
Every term is equal to (d1)/2 with d = 2*u*vv^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



