A097431 Integer part of the hypotenuse of right triangles with consecutive prime legs.

3, 5, 8, 13, 17, 21, 25, 29, 37, 42, 48, 55, 59, 63, 70, 79, 84, 90, 97, 101, 107, 114, 121, 131, 140, 144, 148, 152, 157, 169, 182, 189, 195, 203, 212, 217, 226, 233, 240, 248, 254, 263, 271, 275, 280, 290, 307, 318, 322, 326, 333, 339, 347, 359, 367, 376, 381

Offset: 1

Author

Cino Hilliard, Aug 22 2004

Keywords

• nonn

Examples

			If legs = 3,5 then floor(sqrt(9+25)) = 5, the 2nd entry.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A069484.

Programs

Magma

[Floor(Sqrt(NthPrime(n)^2 + NthPrime(n+1)^2)): n in [1..60]]; // Vincenzo Librandi, Mar 11 2015

Mathematica

Table[Floor[Sqrt[Prime[n]^2 + Prime[n + 1]^2]], {n, 60}] (* Vincenzo Librandi, Mar 11 2015 *)
Floor[Sqrt[Total[#^2]]]&/@Partition[Prime[Range[60]],2,1] (* Harvey P. Dale, Mar 30 2024 *)

PARI

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

Formula

a(n) = floor(sqrt(prime(n)^2 + prime(n+1)^2)) = floor(sqrt(A069484(n))).