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A097433
Integer part of the hypotenuse of prime leg isosceles right triangles.
1
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
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
KEYWORD
nonn
AUTHOR
Cino Hilliard, Aug 22 2004
STATUS
approved