OFFSET
1,2
COMMENTS
This sequence gives the values |x-y| of primitive Pythagorean triangles (x,y,z) with even y ordered according to the nondecreasing values of the leg sums x+y (called w in the Zumkeller link, and given in A198441). For the equivalence to primitive Pythagorean triples with even y see a comment in A198441. - Wolfdieter Lang, May 22 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 triple (x,y,z), y even, connection:
a(2) = 7 because the triple with second smallest leg sum x+y = 17 = A198441(2) is (5,12,13), and |x - y| = y - x = 12 - 5 = 7.
a(3) = 7 because x + y = A198441(3) = 23, (x,y,z) = (15,8,17) (the primitive triple with third smallest leg sum), and |x-y| = x - y = 15 - 8 = 7. (End)
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, 1]] (* Jean-François Alcover, Oct 22 2021 *)
PROG
(Haskell)
a198439 n = a198439_list !! (n-1)
a198439_list = map a198388 a198409_list
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Oct 25 2011
STATUS
approved