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A055527
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Shortest other leg of a Pythagorean triangle with n as length of a leg.
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18
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4, 3, 12, 8, 24, 6, 12, 24, 60, 5, 84, 48, 8, 12, 144, 24, 180, 15, 20, 120, 264, 7, 60, 168, 36, 21, 420, 16, 480, 24, 44, 288, 12, 15, 684, 360, 52, 9, 840, 40, 924, 33, 24, 528, 1104, 14, 168, 120, 68, 39, 1404, 72, 48, 33, 76, 840, 1740, 11, 1860, 960, 16, 48, 72
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OFFSET
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3,1
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COMMENTS
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Least positive k such that n^2 + k^2 is a square.
For odd n, a(n) <= 4*triangular((n-1)/2), because n^2 + (4 * triangular((n-1)/2))^2 = ((n^2+1)/2) ^ 2, which is a perfect square since n is odd.
For n = 4*k+2, a(n) <= 8*triangular(k), because (4k+2)^2 + (4*k*(k+1))^2 = (4*k^2 + 4*k + 2)^2. (End)
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LINKS
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FORMULA
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MATHEMATICA
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Table[k = 1; While[! IntegerQ[Sqrt[n^2 + k^2]], k++]; k, {n, 3, 100}] (* T. D. Noe, Apr 02 2014 *)
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CROSSREFS
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Cf. A000290, A000217, A009112, A046079, A046080, A046081, A054435, A054436, A055522, A055523, A055524, A055525, A055526.
See A082183 for a similar sequence involving triangular numbers.
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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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