A198436 Second term of a triple of squares in arithmetic progression, which is not a multiple of another triple in (A198384, A198385, A198386).

25, 169, 289, 625, 841, 1369, 1681, 3721, 2809, 4225, 4225, 7225, 5329, 7225, 7921, 10201, 12769, 9409, 11881, 15625, 21025, 21025, 22201, 18769, 32761, 24649, 29929, 38809, 34225, 28561, 48841, 34225, 37249, 42025, 52441, 66049, 70225, 42025, 48841, 54289

Offset

1,1

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) = A198440(n)^2 = A198385(A198409(n)).

a(n) - A198435(n) = A198437(n) - a(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, 2]] (* Jean-François Alcover, Oct 20 2021 *)

Prog

(Haskell)
a198436 n = a198436_list !! (n-1)
a198436_list = map a198385 a198409_list

Crossrefs

Cf. A198385, A198409, A198435, A198437, A198438, A198440.

Sequence in context: A324899 A338892 A360280 * A080109 A017126 A007204

Adjacent sequences: A198433 A198434 A198435 * A198437 A198438 A198439

Keyword

nonn

Author

Reinhard Zumkeller, Oct 25 2011

Status

approved