cp's OEIS Frontend

A198435 First term of a triple of squares in arithmetic progression, which is not a multiple of another triple in (A198384,A198385,A198386).

%I A198435 #17 Oct 21 2021 01:35:48
%S A198435 1,49,49,289,1,529,961,2401,289,2209,529,5041,49,1681,1681,6241,9409,
%T A198435 49,961,5329,16129,14161,7921,289,25921,2209,12769,27889,14161,1,
%U A198435 39601,2401,5329,10609,25921,49729,58081,529,961,10609,7921,36481,82369,22801,47089
%N A198435 First term of a triple of squares in arithmetic progression, which is not a multiple of another triple in (A198384,A198385,A198386).
%H A198435 Ray Chandler, <a href="/A198435/b198435.txt">Table of n, a(n) for n = 1..10000</a>
%H A198435 Keith Conrad, <a href="http://www.math.uconn.edu/~kconrad/blurbs/ugradnumthy/3squarearithprog.pdf">Arithmetic progressions of three squares</a>
%H A198435 Reinhard Zumkeller, <a href="/A198435/a198435.txt">Table of initial values</a>
%F A198435 a(n) = A198439(n)^2 = A198384(A198409(n));
%F A198435 A198436(n) - a(n) = A198437(n) - A198436(n) = A198438(n).
%t A198435 wmax = 1000;
%t A198435 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 A198435 tt = Flatten[DeleteCases[triples /@ Range[wmax], {}], 2];
%t A198435 DeleteCases[tt, t_List /; GCD @@ t>1 && MemberQ[tt, t/GCD @@ t]][[All, 1]] (* _Jean-François Alcover_, Oct 20 2021 *)
%o A198435 (Haskell)
%o A198435 a198435 n = a198435_list !! (n-1)
%o A198435 a198435_list = map a198384 a198409_list
%Y A198435 Cf. A198384, A198409, A198437, A198438, A198439
%K A198435 nonn
%O A198435 1,2
%A A198435 _Reinhard Zumkeller_, Oct 25 2011