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A198437
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Third 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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8
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49, 289, 529, 961, 1681, 2209, 2401, 5041, 5329, 6241, 7921, 9409, 10609, 12769, 14161, 14161, 16129, 18769, 22801, 25921, 25921, 27889, 36481, 37249, 39601, 47089, 47089, 49729, 54289, 57121, 58081, 66049, 69169, 73441, 78961, 82369, 82369, 83521, 96721
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listen;
history;
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internal format)
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OFFSET
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1,1
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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) = A198441(n)^2 = A198386(A198409(n));
a(n) - A198436(n) = A198436(n) - A198435(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, 3]] (* Jean-François Alcover, Oct 20 2021 *)
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PROG
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(Haskell)
a198437 n = a198437_list !! (n-1)
a198437_list = map a198386 a198409_list
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CROSSREFS
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Cf. A198435, A198436, A198438, A198409, A198441.
Sequence in context: A219030 A167719 A239211 * A144407 A089552 A017354
Adjacent sequences: A198434 A198435 A198436 * A198438 A198439 A198440
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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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