A088546 - OEIS

%I #17 Mar 05 2020 04:56:09

%S 7,17,23,31,47,41,49,71,73,79,89,97,113,103,119,119,127,137,151,161,

%T 161,167,191,199,193,217,217,233,223,241,263,271,257,239,281,287,287,

%U 313,289,329,329,343,311,353,367,337,359,383,409,391,401,391,433,439,463

%N Square root of sum of legs of primitive Pythagorean triangles having legs that add up to a square, sorted on hypotenuse.

%C Numbers whose square is the sum of the legs of primitive Pythagorean triangles with hypotenuse A088319(n).

%H Ray Chandler, <a href="/A088546/b088546.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = abs(j^2 - k^2/2), where j=A088515(n), k=A088516(n).

%F a(n) = sqrt(A089552(n)).

%e 31 is in the sequence because it is associated with the primitive Pythagorean triangle (400,561,689) where 400+561=31^2.

%t terms = 1000; jmax = 100; kmax = 200;

%t Reap[Do[If[CoprimeQ[j, k], e = j^2 - j k + k^2/2; f = j k; If[e > f, Sow[{e^2 + f^2, Abs[j^2 - k^2/2]}]]], {j, 1, jmax}, {k, 2, kmax, 2}]][[2, 1]] // Sort // #[[;; terms, 2]]& (* _Jean-François Alcover_, Mar 05 2020 *)

%Y Cf. A088319, A088515, A088516, A089545-A089552, A089554-A089558.

%K nonn

%O 1,1

%A _Lekraj Beedassy_, Nov 17 2003

%E More terms from _Ray Chandler_, Nov 16 2003