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

1,1

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

a(n) - A198436(n) = A198436(n) - A198435(n) = A198438(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];
DeleteCases[tt, t_List /; GCD @@ t>1 && MemberQ[tt, t/GCD @@ t]][[All, 3]] (* _Jean-François Alcover_, Oct 20 2021 *)

Prog

(Haskell)
a198437 n = a198437_list !! (n-1)
a198437_list = map a198386 a198409_list

Crossrefs

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

Sequence in context: A219030 A167719 A239211 * A144407 A089552 A017354

Adjacent sequences: A198434 A198435 A198436 * A198438 A198439 A198440

Keyword

nonn

Author

_Reinhard Zumkeller_, Oct 25 2011

Status

approved