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

1,1

Links

Table of n, a(n) for n=1..71.

Formula

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

Example

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

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 *)

Prog

(PARI) f(n) = for(j=1, n, my(x=j, y=j+1); print1(sqrtint(x^2+y^2)", "))

Crossrefs

Cf. A000196, A001844, A001951.

Sequence in context: A195121 A047332 A248233 * A364153 A230391 A284931

Adjacent sequences: A097429 A097430 A097431 * A097433 A097434 A097435

Keyword

nonn,easy

Author

Cino Hilliard, Aug 22 2004

Status

approved