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

1,2

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) = A198388(n)^2.

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

A198435(n) = a(A198409(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]];
Flatten[DeleteCases[triples /@ Range[wmax], {}], 2][[All, 1]] (* Jean-François Alcover, Oct 19 2021 *)

Prog

(Haskell)
a198384 n = a198384_list !! (n-1)
a198384_list = map (^ 2) a198388_list

Crossrefs

Sequence in context: A189347 A248558 A372052 * A136196 A222960 A061100

Adjacent sequences: A198381 A198382 A198383 * A198385 A198386 A198387

Keyword

nonn

Author

Reinhard Zumkeller, Oct 24 2011

Extensions

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

Status

approved