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A198435
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First term of a triple of squares in arithmetic progression, which is not a multiple of another triple in (A198384,A198385,A198386).
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9
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1, 49, 49, 289, 1, 529, 961, 2401, 289, 2209, 529, 5041, 49, 1681, 1681, 6241, 9409, 49, 961, 5329, 16129, 14161, 7921, 289, 25921, 2209, 12769, 27889, 14161, 1, 39601, 2401, 5329, 10609, 25921, 49729, 58081, 529, 961, 10609, 7921, 36481, 82369, 22801, 47089
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OFFSET
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1,2
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LINKS
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Ray Chandler, Table of n, a(n) for n = 1..10000
Keith Conrad, Arithmetic progressions of three squares
Reinhard Zumkeller, Table of initial values
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FORMULA
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a(n) = A198439(n)^2 = A198384(A198409(n));
A198436(n) - a(n) = A198437(n) - A198436(n) = A198438(n).
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MATHEMATICA
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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, 1]] (* Jean-François Alcover, Oct 20 2021 *)
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PROG
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(Haskell)
a198435 n = a198435_list !! (n-1)
a198435_list = map a198384 a198409_list
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CROSSREFS
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Cf. A198384, A198409, A198437, A198438, A198439
Sequence in context: A291480 A255426 A090094 * A165870 A266803 A050709
Adjacent sequences: A198432 A198433 A198434 * A198436 A198437 A198438
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller, Oct 25 2011
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STATUS
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approved
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