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%I #15 Mar 04 2020 11:07:15
%S 41,205,389,689,1565,1625,1781,3865,4105,4549,5989,7421,9161,9685,
%T 10225,10685,13025,17509,17965,18329,21349,21701,25801,33161,33169,
%U 33529,36749,38581,39709,49325,51649,52429,52721,56785,57065,67205,70801
%N Ordered hypotenuses of primitive Pythagorean triangles having legs that add up to a square.
%D F. Rubin, "Squared" Pythagorean Triples, Solution to problem 2306, J. Recreational Mathematics, Vol. 29, No. 1, 1998, p. 73.
%H Ray Chandler, <a href="/A088319/b088319.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n)=e^2+f^2, where e>f, e=j^2 - jk + k^2/2 and f=jk for coprime pairs (j, k) with k even.
%e 9161 is in the sequence because of the triple 5289^2 + 7480^2 = 9161^2 where we have 5289+7480=113^2.
%e Similarly, 205 belongs to the triple (133,156,205) and 133+156=17^2.
%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]]], {j, 1, jmax}, {k, 2, kmax, 2}]][[2, 1]] // Union // Take[#, terms]& (* _Jean-François Alcover_, Mar 04 2020 *)
%Y Cf. A088515, A088516, A088546, A089545-A089552, A089554-A089558.
%K nonn
%O 1,1
%A _Lekraj Beedassy_, Nov 06 2003
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