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A106499
Ordered perimeter of primitive integer-sided triangle one of whose angles is twice another.
12
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
KEYWORD
nonn
AUTHOR
Lekraj Beedassy, May 04 2005
EXTENSIONS
Extended by Ray Chandler, May 09 2005
STATUS
approved