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

1,2

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

Formula

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A050090 A152004 A298862 * A330072 A213510 A130257

Adjacent sequences: A198406 A198407 A198408 * A198410 A198411 A198412

Keyword

nonn

Author

Reinhard Zumkeller, Oct 25 2011

Status

approved