A097432 Integer part of the hypotenuse of right triangles with consecutive integer legs.

2, 3, 5, 6, 7, 9, 10, 12, 13, 14, 16, 17, 19, 20, 21, 23, 24, 26, 27, 29, 30, 31, 33, 34, 36, 37, 38, 40, 41, 43, 44, 45, 47, 48, 50, 51, 53, 54, 55, 57, 58, 60, 61, 62, 64, 65, 67, 68, 70, 71, 72, 74, 75, 77, 78, 79, 81, 82, 84, 85, 86, 88, 89, 91, 92, 94, 95, 96, 98, 99, 101

Offset: 1

Author

Cino Hilliard, Aug 22 2004

Keywords

• nonn

Examples

			If legs = 3,4 then hypot = floor(sqrt(9+16)) = 5, the 3rd term.
		

Crossrefs

Cf. A001951.

Programs

Maple

A097432 := proc(n)
    floor(sqrt(n^2+(n+1)^2)) ;
end proc: # R. J. Mathar, Oct 04 2018

Mathematica

Table[Floor[Sqrt[n^2+(n+1)^2]],{n,100}]  (* Harvey P. Dale, Apr 02 2011 *)

PARI

f(n) = for(j=1,n,x=j;y=j+1;print1(floor(sqrt(x^2+y^2))","))

Formula

a(n) = floor(sqrt(n^2 + (n+1)^2)) = floor(sqrt(A001844(n))).