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 A198439 Square root of first term of a triple of squares in arithmetic progression that is not a multiple of another triple in (A198384, A198385, A198386). 6
 1, 7, 7, 17, 1, 23, 31, 49, 17, 47, 23, 71, 7, 41, 41, 79, 97, 7, 31, 73, 127, 119, 89, 17, 161, 47, 113, 167, 119, 1, 199, 49, 73, 103, 161, 223, 241, 23, 31, 103, 89, 191, 287, 151, 217, 287, 137, 233, 71, 337, 79, 137, 17, 281, 359, 391, 49, 113, 119, 217 (list; graph; refs; listen; history; text; internal format)
 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 FORMULA A198435(n) = a(n)^2; a(n) = A198388(A198409(n)). 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}]]]]][]; 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 Sequence in context: A168411 A120682 A152910 * A100635 A292084 A168458 Adjacent sequences:  A198436 A198437 A198438 * A198440 A198441 A198442 KEYWORD nonn AUTHOR Reinhard Zumkeller, Oct 25 2011 STATUS approved

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Last modified July 4 08:01 EDT 2022. Contains 355070 sequences. (Running on oeis4.)