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A198384 First of a triple of squares in arithmetic progression.

%I A198384 #36 Oct 20 2021 09:24:01
%S A198384 1,4,49,9,49,16,289,196,25,1,36,196,529,49,961,441,64,1156,81,784,441,
%T A198384 100,2401,289,121,2209,4,144,1225,529,169,784,2601,2116,5041,196,3844,
%U A198384 1764,49,225,256,1681,1225,289,1681,2401,6241,9,4624,324,9409,361
%N A198384 First of a triple of squares in arithmetic progression.
%H A198384 Ray Chandler, <a href="/A198384/b198384.txt">Table of n, a(n) for n = 1..10000</a>
%H A198384 Keith Conrad, <a href="http://www.math.uconn.edu/~kconrad/blurbs/ugradnumthy/3squarearithprog.pdf">Arithmetic progressions of three squares</a>
%H A198384 Reinhard Zumkeller, <a href="/A198384/a198384_2.txt">Table of initial values</a>
%F A198384 a(n) = A198388(n)^2.
%F A198384 A198385(n) - a(n) = A198386(n) - A198385(n) = A198387(n).
%F A198384 A198435(n) = a(A198409(n)).
%t A198384 wmax = 1000;
%t A198384 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 A198384 Flatten[DeleteCases[triples /@ Range[wmax], {}], 2][[All, 1]] (* _Jean-François Alcover_, Oct 19 2021 *)
%o A198384 (Haskell)
%o A198384 a198384 n = a198384_list !! (n-1)
%o A198384 a198384_list = map (^ 2) a198388_list
%K A198384 nonn
%O A198384 1,2
%A A198384 _Reinhard Zumkeller_, Oct 24 2011
%E A198384 Thanks to _Benoit Jubin_, who had the idea for sequences A198384 .. A198390 and A198435 .. A198441.