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

Author

Lekraj Beedassy, May 04 2005

Keywords

• nonn

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

Crossrefs

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

Programs

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 *)

Formula

a(n)=s*(r+s), where r

Extensions

Extended by Ray Chandler, May 09 2005

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