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A198388
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Square root of first term of a triple of squares in arithmetic progression.
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5
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1, 2, 7, 3, 7, 4, 17, 14, 5, 1, 6, 14, 23, 7, 31, 21, 8, 34, 9, 28, 21, 10, 49, 17, 11, 47, 2, 12, 35, 23, 13, 28, 51, 46, 71, 14, 62, 42, 7, 15, 16, 41, 35, 17, 41, 49, 79, 3, 68, 18, 97, 19, 56, 7, 42, 20, 69, 98, 34, 21, 93, 31, 63, 22, 85, 94, 23, 49, 73
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OFFSET
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1,2
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COMMENTS
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There is a connection to |x-y| of Pythagorean triangles (x,y,z). See a comment on the primitive Pythagorean triangle case under A198441 which applies mutatis mutandis. - Wolfdieter Lang, May 23 2013
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LINKS
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FORMULA
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EXAMPLE
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Connection to Pythagorean triangles: a(2) = 2 because (in the notation of the Zumkeller link) (u,v,w) = 2*(1,5,7) and the corresponding Pythagorean triangle is 2*((7-1)/2,(1+7)/2,5) = 2*(3,4,5) with |x-y| = 2*(4-3) = 2. - Wolfdieter Lang, May 23 2013
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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, v, w}]]]]][[2]];
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PROG
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(Haskell)
a198388 n = a198388_list !! (n-1)
a198388_list = map (\(x, _, _) -> x) ts where
ts = [(u, v, w) | w <- [1..], v <- [1..w-1], u <- [1..v-1],
w^2 - v^2 == v^2 - u^2]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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