A198409 - OEIS

%I #16 Oct 24 2021 12:33:58

%S 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 88,97,98,102,107,114,115,124,126,129,136,141,142,143,156,157,167,169,

%U 172,177,181,188,191,201,205,208,214,218,229,230,237,244,249,253

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

%C A198435(n) = A198384(a(n)); A198439(n) = A198388(a(n));

%C A198436(n) = A198385(a(n)); A198440(n) = A198389(a(n));

%C A198437(n) = A198386(a(n)); A198441(n) = A198390(a(n));

%C A198438(n) = A198387(a(n)).

%H Ray Chandler, <a href="/A198409/b198409.txt">Table of n, a(n) for n = 1..10000</a>

%H Reinhard Zumkeller, <a href="/A198435/a198435.txt">Table of initial values</a>

%F A008966(A050873(A198439(n),A050873(A198440(n),A050873(A198441(n))))) = 1.

%t wmax = 1000;

%t 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 tt = Flatten[DeleteCases[triples /@ Range[wmax], {}], 2];

%t Position[tt, t_List /; SquareFreeQ[GCD@@t]] // Flatten (* _Jean-François Alcover_, Oct 24 2021 *)

%o (Haskell)

%o import Data.List (elemIndices)

%o a198409 n = a198409_list !! (n-1)

%o a198409_list = map (+ 1) $ elemIndices 1 $ map a008966 $

%o    zipWith gcd a198384_list $ zipWith gcd a198385_list a198386_list

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Oct 25 2011