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A198384
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First of a triple of squares in arithmetic progression.
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15
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1, 4, 49, 9, 49, 16, 289, 196, 25, 1, 36, 196, 529, 49, 961, 441, 64, 1156, 81, 784, 441, 100, 2401, 289, 121, 2209, 4, 144, 1225, 529, 169, 784, 2601, 2116, 5041, 196, 3844, 1764, 49, 225, 256, 1681, 1225, 289, 1681, 2401, 6241, 9, 4624, 324, 9409, 361
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listen;
history;
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internal format)
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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) = A198388(n)^2.
A198385(n) - a(n) = A198386(n) - A198385(n) = A198387(n).
A198435(n) = a(A198409(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]];
Flatten[DeleteCases[triples /@ Range[wmax], {}], 2][[All, 1]] (* Jean-François Alcover, Oct 19 2021 *)
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PROG
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(Haskell)
a198384 n = a198384_list !! (n-1)
a198384_list = map (^ 2) a198388_list
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CROSSREFS
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Sequence in context: A058311 A189347 A248558 * A136196 A222960 A061100
Adjacent sequences: A198381 A198382 A198383 * A198385 A198386 A198387
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller, Oct 24 2011
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EXTENSIONS
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Thanks to Benoit Jubin, who had the idea for sequences A198384 .. A198390 and A198435 .. A198441.
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STATUS
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approved
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