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A198409 Positions in sequences A198384, A198385 and A198386 to indicate triples of squares in arithmetic progression, that are not multiples of earlier triples.

%I A198409 #16 Oct 24 2021 12:33:58
%S A198409 1,3,5,7,10,13,15,23,24,26,30,35,39,42,45,47,51,54,62,69,70,72,83,84,
%T A198409 88,97,98,102,107,114,115,124,126,129,136,141,142,143,156,157,167,169,
%U A198409 172,177,181,188,191,201,205,208,214,218,229,230,237,244,249,253
%N A198409 Positions in sequences A198384, A198385 and A198386 to indicate triples of squares in arithmetic progression, that are not multiples of earlier triples.
%C A198409 A198435(n) = A198384(a(n)); A198439(n) = A198388(a(n));
%C A198409 A198436(n) = A198385(a(n)); A198440(n) = A198389(a(n));
%C A198409 A198437(n) = A198386(a(n)); A198441(n) = A198390(a(n));
%C A198409 A198438(n) = A198387(a(n)).
%H A198409 Ray Chandler, <a href="/A198409/b198409.txt">Table of n, a(n) for n = 1..10000</a>
%H A198409 Reinhard Zumkeller, <a href="/A198435/a198435.txt">Table of initial values</a>
%F A198409 A008966(A050873(A198439(n),A050873(A198440(n),A050873(A198441(n))))) = 1.
%t A198409 wmax = 1000;
%t A198409 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 A198409 tt = Flatten[DeleteCases[triples /@ Range[wmax], {}], 2];
%t A198409 Position[tt, t_List /; SquareFreeQ[GCD@@t]] // Flatten (* _Jean-François Alcover_, Oct 24 2021 *)
%o A198409 (Haskell)
%o A198409 import Data.List (elemIndices)
%o A198409 a198409 n = a198409_list !! (n-1)
%o A198409 a198409_list = map (+ 1) $ elemIndices 1 $ map a008966 $
%o A198409    zipWith gcd a198384_list $ zipWith gcd a198385_list a198386_list
%K A198409 nonn
%O A198409 1,2
%A A198409 _Reinhard Zumkeller_, Oct 25 2011