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

1, 49, 49, 289, 1, 529, 961, 2401, 289, 2209, 529, 5041, 49, 1681, 1681, 6241, 9409, 49, 961, 5329, 16129, 14161, 7921, 289, 25921, 2209, 12769, 27889, 14161, 1, 39601, 2401, 5329, 10609, 25921, 49729, 58081, 529, 961, 10609, 7921, 36481, 82369, 22801, 47089

Offset

1,2

Links

Ray Chandler, Table of n, a(n) for n = 1..10000

Keith Conrad, Arithmetic progressions of three squares

Reinhard Zumkeller, Table of initial values

Formula

a(n) = A198439(n)^2 = A198384(A198409(n));

A198436(n) - a(n) = A198437(n) - A198436(n) = A198438(n).

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];
DeleteCases[tt, t_List /; GCD @@ t>1 && MemberQ[tt, t/GCD @@ t]][[All, 1]] (* Jean-François Alcover, Oct 20 2021 *)

Prog

(Haskell)
a198435 n = a198435_list !! (n-1)
a198435_list = map a198384 a198409_list

Crossrefs

Cf. A198384, A198409, A198437, A198438, A198439

Sequence in context: A291480 A255426 A090094 * A165870 A266803 A050709

Adjacent sequences: A198432 A198433 A198434 * A198436 A198437 A198438

Keyword

nonn

Author

Reinhard Zumkeller, Oct 25 2011

Status

approved