A106499 Ordered perimeter of primitive integer-sided triangle one of whose angles is twice another.

15, 28, 40, 45, 66, 77, 84, 91, 104, 120, 126, 144, 153, 170, 187, 190, 198, 209, 220, 228, 231, 260, 273, 276, 286, 299, 312, 322, 325, 345, 350, 378, 390, 400, 420, 432, 435, 442, 459, 464, 476, 493, 496, 510, 522, 527, 544, 551, 558, 561, 570, 589, 608

Offset

1,1

Comments

For corresponding values of r and s, see A106500 and A106501.

The sides of the primitive triangle are given by the triple (r*s,s^2 - r^2,r^2).

Links

Jean-François Alcover, Table of n, a(n) for n = 1..869

Formula

a(n)=s*(r+s), where r<s<2r and (r, s)=1.

Mathematica

s[p_] := Solve[1 < r < s < 2r && p == r s + s^2 && GCD[r, s] == 1, {r, s}, Integers];
Reap[For[p = 1, p <= 10000, p++, sp = s[p]; If[sp =!= {}, Sow[p]; Print[p, " ", {r s, s^2 - r^2, r^2} /. sp[[1]]]]]][[2, 1]] (* Jean-François Alcover, Mar 06 2020 *)

Crossrefs

Cf. A106500-A106506, A106410, A106420, A106430.

Sequence in context: A291054 A134621 A373259 * A043108 A045192 A039285

Adjacent sequences: A106496 A106497 A106498 * A106500 A106501 A106502

Keyword

nonn

Author

Lekraj Beedassy, May 04 2005

Extensions

Extended by Ray Chandler, May 09 2005

Status

approved