A216260 Hypotenuse of the smallest Pythagorean triple whose legs are m and 2m + n.

305, 13, 915, 26, 85, 39, 2135, 52, 2745, 25, 37, 78, 3965, 91, 255, 104, 5185, 117, 205, 50, 6405, 41, 7015, 156, 425, 169, 8235, 182, 125, 75, 65, 208, 111, 221, 595, 234, 11285, 61, 11895, 100, 377, 273, 13115, 82, 765, 299, 14335, 312, 14945, 125

Offset

1,1

Comments

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).

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Example

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.

Mathematica

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 *)

Crossrefs

Sequence in context: A281329 A293092 A221117 * A160577 A256603 A058828

Adjacent sequences: A216257 A216258 A216259 * A216261 A216262 A216263

Keyword

nonn

Author

Elliott Line, Mar 15 2013

Status

approved