A198384 First of a triple of squares in arithmetic progression.

1, 4, 49, 9, 49, 16, 289, 196, 25, 1, 36, 196, 529, 49, 961, 441, 64, 1156, 81, 784, 441, 100, 2401, 289, 121, 2209, 4, 144, 1225, 529, 169, 784, 2601, 2116, 5041, 196, 3844, 1764, 49, 225, 256, 1681, 1225, 289, 1681, 2401, 6241, 9, 4624, 324, 9409, 361

Offset: 1

Author

Reinhard Zumkeller, Oct 24 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

Programs

Haskell

a198384 n = a198384_list !! (n-1)
a198384_list = map (^ 2) a198388_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]];
Flatten[DeleteCases[triples /@ Range[wmax], {}], 2][[All, 1]] (* Jean-François Alcover, Oct 19 2021 *)

Formula

a(n) = A198388(n)^2.

A198385(n) - a(n) = A198386(n) - A198385(n) = A198387(n).

A198435(n) = a(A198409(n)).

Extensions

Thanks to Benoit Jubin, who had the idea for sequences A198384 .. A198390 and A198435 .. A198441.