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

1,1

Links

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

Formula

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

Example

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

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 *)

Prog

(PARI) a(n) = for(j=1, n, x=prime(j); y=prime(j+1); print1(floor(sqrt(x^2+y^2))", "))
(Magma) [Floor(Sqrt(NthPrime(n)^2 + NthPrime(n+1)^2)): n in [1..60]]; // Vincenzo Librandi, Mar 11 2015

Crossrefs

Cf. A069484.

Sequence in context: A357048 A331467 A337289 * A123929 A036715 A337503

Adjacent sequences: A097428 A097429 A097430 * A097432 A097433 A097434

Keyword

nonn

Author

Cino Hilliard, Aug 22 2004

Status

approved