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%I #14 Mar 16 2013 08:27:18
%S 305,13,915,26,85,39,2135,52,2745,25,37,78,3965,91,255,104,5185,117,
%T 205,50,6405,41,7015,156,425,169,8235,182,125,75,65,208,111,221,595,
%U 234,11285,61,11895,100,377,273,13115,82,765,299,14335,312,14945,125
%N Hypotenuse of the smallest Pythagorean triple whose legs are m and 2m + n.
%C a(n) where n is divisible by k will not exceed a(k)*n/k. A consequence of this is that even if n is prime, a(n) will not exceed 305n (since a(1) = 305).
%H Giovanni Resta, <a href="/A216260/b216260.txt">Table of n, a(n) for n = 1..10000</a>
%e a(17) = 5185 because the smallest Pythagorean triple whose legs are m and 2m + 17 has hypotenuse 5185. m in this case = 2312, and 2m + 17 = 4641.
%t a[n_] := Block[{k = 1, h}, While[h = 5*k^2 + 4*k*n + n^2; Round[Sqrt@N@h]^2 != h, k++]; Sqrt@h]; Array[a, 50] (* _Giovanni Resta_, Mar 15 2013 *)
%K nonn
%O 1,1
%A _Elliott Line_, Mar 15 2013
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