A198438 Common differences in triples of squares in arithmetic progression, that are not a multiples of other triples in (A198384, A198385, A198386).

24, 120, 240, 336, 840, 840, 720, 1320, 2520, 2016, 3696, 2184, 5280, 5544, 6240, 3960, 3360, 9360, 10920, 10296, 4896, 6864, 14280, 18480, 6840, 22440, 17160, 10920, 20064, 28560, 9240, 31824, 31920, 31416, 26520, 16320, 12144, 41496, 47880, 43680, 50160

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) = A198387(A198409(n)) = A198436(n) - A198435(n) = A198437(n) - A198436(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];
#[[2]] - #[[1]]& /@ DeleteCases[tt, t_List /; GCD@@t > 1 && MemberQ[tt, t/GCD@@t]] (* Jean-François Alcover, Oct 22 2021 *)

Prog

(Haskell)
a198438 n = a198438_list !! (n-1)
a198438_list = map a198387 a198409_list

Crossrefs

Sequence in context: A293893 A137799 A369541 * A256629 A114200 A229567

Adjacent sequences: A198435 A198436 A198437 * A198439 A198440 A198441

Keyword

nonn

Author

Reinhard Zumkeller, Oct 25 2011

Status

approved