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A198437 Third term of a triple of squares in arithmetic progression, which is not a multiple of another triple in (A198384,A198385,A198386).

%I A198437 #14 Oct 20 2021 12:20:50
%S A198437 49,289,529,961,1681,2209,2401,5041,5329,6241,7921,9409,10609,12769,
%T A198437 14161,14161,16129,18769,22801,25921,25921,27889,36481,37249,39601,
%U A198437 47089,47089,49729,54289,57121,58081,66049,69169,73441,78961,82369,82369,83521,96721
%N A198437 Third term of a triple of squares in arithmetic progression, which is not a multiple of another triple in (A198384,A198385,A198386).
%H A198437 Ray Chandler, <a href="/A198437/b198437.txt">Table of n, a(n) for n = 1..10000</a>
%H A198437 Keith Conrad, <a href="http://www.math.uconn.edu/~kconrad/blurbs/ugradnumthy/3squarearithprog.pdf">Arithmetic progressions of three squares</a>
%H A198437 Reinhard Zumkeller, <a href="/A198435/a198435.txt">Table of initial values</a>
%F A198437 a(n) = A198441(n)^2 = A198386(A198409(n));
%F A198437 a(n) - A198436(n) = A198436(n) - A198435(n) = A198438(n).
%t A198437 wmax = 1000;
%t A198437 triples[w_] := Reap[Module[{u, v}, For[u = 1, u < w, u++, If[IntegerQ[v = Sqrt[(u^2 + w^2)/2]], Sow[{u^2, v^2, w^2}]]]]][[2]];
%t A198437 tt = Flatten[DeleteCases[triples /@ Range[wmax], {}], 2];
%t A198437 DeleteCases[tt, t_List /; GCD @@ t>1 && MemberQ[tt, t/GCD @@ t]][[All, 3]] (* _Jean-François Alcover_, Oct 20 2021 *)
%o A198437 (Haskell)
%o A198437 a198437 n = a198437_list !! (n-1)
%o A198437 a198437_list = map a198386 a198409_list
%Y A198437 Cf. A198435, A198436, A198438, A198409, A198441.
%K A198437 nonn
%O A198437 1,1
%A A198437 _Reinhard Zumkeller_, Oct 25 2011