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

1, 3, 5, 7, 10, 13, 15, 23, 24, 26, 30, 35, 39, 42, 45, 47, 51, 54, 62, 69, 70, 72, 83, 84, 88, 97, 98, 102, 107, 114, 115, 124, 126, 129, 136, 141, 142, 143, 156, 157, 167, 169, 172, 177, 181, 188, 191, 201, 205, 208, 214, 218, 229, 230, 237, 244, 249, 253

Offset: 1

Author

Reinhard Zumkeller, Oct 25 2011

Keywords

• nonn

Comments

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

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

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

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

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000
• Reinhard Zumkeller, Table of initial values

Programs

Haskell

import Data.List (elemIndices)
a198409 n = a198409_list !! (n-1)
a198409_list = map (+ 1) $ elemIndices 1 $ map a008966 $
   zipWith gcd a198384_list $ zipWith gcd a198385_list a198386_list

Mathematica

wmax = 1000;
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]];
tt = Flatten[DeleteCases[triples /@ Range[wmax], {}], 2];
Position[tt, t_List /; SquareFreeQ[GCD@@t]] // Flatten (* Jean-François Alcover, Oct 24 2021 *)

Formula

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