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A055527 Shortest other leg of a Pythagorean triangle with n as length of a leg. 16
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

COMMENTS

From Alex Ratushnyak, Mar 30 2014: (Start)

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)

LINKS

T. D. Noe, Table of n, a(n) for n = 3..1000

FORMULA

a(n) = sqrt(A055526(n)^2-n^2) = 2*A054436/n.

MAPLE

P:=proc(n) local k; k:=1;

while frac(evalf(sqrt(n^2+k^2)))>0 do k:=k+1; od; k;

end: seq(P(i), i=3..65); # Paolo P. Lava, Dec 10 2018

MATHEMATICA

Table[k = 1; While[! IntegerQ[Sqrt[n^2 + k^2]], k++]; k, {n, 3, 100}] (* T. D. Noe, Apr 02 2014 *)

CROSSREFS

Cf. A000290, A000217, A009112, A046079, A046080, A046081, A054435, A054436, A055522, A055523, A055524, A055525, A055526.

Sequence in context: A327916 A270025 A271199 * A055523 A168430 A074324

Adjacent sequences:  A055524 A055525 A055526 * A055528 A055529 A055530

KEYWORD

nonn

AUTHOR

Henry Bottomley, May 22 2000

STATUS

approved

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Last modified October 22 15:57 EDT 2019. Contains 328318 sequences. (Running on oeis4.)