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 A198440 Square root of second term of a triple of squares in arithmetic progression that is not a multiple of another triple in (A198384, A198385, A198386). 5
 5, 13, 17, 25, 29, 37, 41, 61, 53, 65, 65, 85, 73, 85, 89, 101, 113, 97, 109, 125, 145, 145, 149, 137, 181, 157, 173, 197, 185, 169, 221, 185, 193, 205, 229, 257, 265, 205, 221, 233, 241, 269, 313, 265, 293, 325, 277, 317, 281, 365, 289, 305, 305, 365, 401 (list; graph; refs; listen; history; text; internal format)
 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 FORMULA A198436(n) = a(n)^2; a(n) = A198389(A198409(n)). EXAMPLE From Wolfdieter Lang, May 22 2013: (Start) Primitive Pythagorean triangle (x,y,z), even y, connection: a(8) = 61 because the leg sum x+y = A198441(8) = 71 and due to A198439(8) = 49 one has y = (71+49)/2 = 60 is even, hence x = (71-49)/2 = 11 and z = sqrt(11^2 + 60^2) = 61. (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, 2]] (* Jean-François Alcover, Oct 22 2021 *) PROG (Haskell) a198440 n = a198440_list !! (n-1) a198440_list = map a198389 a198409_list CROSSREFS Cf. A020882, A222946. Sequence in context: A008846 A162597 A120960 * A094194 A088511 A089545 Adjacent sequences:  A198437 A198438 A198439 * A198441 A198442 A198443 KEYWORD nonn AUTHOR Reinhard Zumkeller, Oct 25 2011 STATUS approved

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Last modified July 3 03:28 EDT 2022. Contains 355030 sequences. (Running on oeis4.)