A097433 Integer part of the hypotenuse of prime leg isosceles right triangles.

2, 4, 7, 9, 15, 18, 24, 26, 32, 41, 43, 52, 57, 60, 66, 74, 83, 86, 94, 100, 103, 111, 117, 125, 137, 142, 145, 151, 154, 159, 179, 185, 193, 196, 210, 213, 222, 230, 236, 244, 253, 255, 270, 272, 278, 281, 298, 315, 321, 323, 329, 337, 340, 354, 363, 371, 380

Offset

1,1

Comments

The real part of these numbers is irrational.

References

Gareth A. Jones and J. Mary Jones, Elementary Number Theory, Springer, 1998; pp. 221-222.

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Formula

a(n) = floor(sqrt(2*p(n)^2)), where p(n) = n-th prime. - N. J. A. Sloane, Feb 23 2015

Mathematica

Floor[Sqrt[2*Prime[Range[80]]^2]] (* Wesley Ivan Hurt, Dec 02 2021 *)

Prog

(PARI) forprime(j=1, 400, print1(floor(sqrt(2*j^2))", "));
(Magma) [Floor(Sqrt(2*p^2)): p in PrimesUpTo(300)]; // G. C. Greubel, Jun 11 2024
(SageMath) [floor(sqrt(2*p^2)) for p in prime_range(1, 300)] # G. C. Greubel, Jun 11 2024

Crossrefs

Sequence in context: A039904 A115162 A278977 * A308758 A110078 A257064

Adjacent sequences: A097430 A097431 A097432 * A097434 A097435 A097436

Keyword

nonn

Author

Cino Hilliard, Aug 22 2004

Status

approved