A198387 Common differences in triples of squares in arithmetic progression.

24, 96, 120, 216, 240, 384, 336, 480, 600, 840, 864, 960, 840, 1176, 720, 1080, 1536, 1344, 1944, 1920, 2160, 2400, 1320, 2520, 2904, 2016, 3360, 3456, 3000, 3696, 4056, 3840, 3024, 3360, 2184, 4704, 2880, 4320, 5280, 5400, 6144, 5544, 6000, 6936, 6240, 5880

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) = A198385(n) - A198384(n) = A198386(n) - A198385(n).

A198438(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]];
#[[2]] - #[[1]]& /@ Flatten[DeleteCases[triples /@ Range[wmax], {}] , 2] (* Jean-François Alcover, Oct 21 2021 *)

Prog

(Haskell)
a198387 n = a198387_list !! (n-1)
a198387_list = zipWith (-) a198385_list a198384_list

Crossrefs

Sequence in context: A208984 A103251 A256418 * A057102 A057103 A055669

Adjacent sequences: A198384 A198385 A198386 * A198388 A198389 A198390

Keyword

nonn

Author

Reinhard Zumkeller, Oct 24 2011

Status

approved