OFFSET
1,1
COMMENTS
This sequence gives the hypotenuses of primitive Pythagorean triangles (with multiplicities) ordered according to nondecreasing values of the leg sums x+y (called w in the Zumkeller link, given by A198441). See the comment on the equivalence to primitive Pythagorean triangles in A198441. For the values of these hypotenuses ordered nondecreasingly see A020882. See also the triangle version A222946. - Wolfdieter Lang, May 23 2013
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
EXAMPLE
From Wolfdieter Lang, May 22 2013: (Start)
Primitive Pythagorean triangle (x,y,z), even y, connection:
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, v, w}]]]]][[2]];
tt = Flatten[DeleteCases[triples /@ Range[wmax], {}], 2];
DeleteCases[tt, t_List /; GCD@@t > 1 && MemberQ[tt, t/GCD@@t]][[All, 2]] (* Jean-François Alcover, Oct 22 2021 *)
PROG
(Haskell)
a198440 n = a198440_list !! (n-1)
a198440_list = map a198389 a198409_list
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Oct 25 2011
STATUS
approved