A198437 Third term of a triple of squares in arithmetic progression, which is not a multiple of another triple in (A198384,A198385,A198386).

49, 289, 529, 961, 1681, 2209, 2401, 5041, 5329, 6241, 7921, 9409, 10609, 12769, 14161, 14161, 16129, 18769, 22801, 25921, 25921, 27889, 36481, 37249, 39601, 47089, 47089, 49729, 54289, 57121, 58081, 66049, 69169, 73441, 78961, 82369, 82369, 83521, 96721

Offset: 1

Author

Reinhard Zumkeller, Oct 25 2011

Keywords

• nonn

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

Crossrefs

Cf. A198435, A198436, A198438, A198409, A198441.

Programs

Haskell

a198437 n = a198437_list !! (n-1)
a198437_list = map a198386 a198409_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];
DeleteCases[tt, t_List /; GCD @@ t>1 && MemberQ[tt, t/GCD @@ t]][[All, 3]] (* Jean-François Alcover, Oct 20 2021 *)

Formula

a(n) = A198441(n)^2 = A198386(A198409(n));

a(n) - A198436(n) = A198436(n) - A198435(n) = A198438(n).