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Integer part of the hypotenuse of prime leg isosceles right triangles.
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%I #18 Jun 11 2024 19:11:11

%S 2,4,7,9,15,18,24,26,32,41,43,52,57,60,66,74,83,86,94,100,103,111,117,

%T 125,137,142,145,151,154,159,179,185,193,196,210,213,222,230,236,244,

%U 253,255,270,272,278,281,298,315,321,323,329,337,340,354,363,371,380

%N Integer part of the hypotenuse of prime leg isosceles right triangles.

%C The real part of these numbers is irrational.

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

%H G. C. Greubel, <a href="/A097433/b097433.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = floor(sqrt(2*p(n)^2)), where p(n) = n-th prime. - _N. J. A. Sloane_, Feb 23 2015

%t Floor[Sqrt[2*Prime[Range[80]]^2]] (* _Wesley Ivan Hurt_, Dec 02 2021 *)

%o (PARI) forprime(j=1,400,print1(floor(sqrt(2*j^2))","));

%o (Magma) [Floor(Sqrt(2*p^2)): p in PrimesUpTo(300)]; // _G. C. Greubel_, Jun 11 2024

%o (SageMath) [floor(sqrt(2*p^2)) for p in prime_range(1,300)] # _G. C. Greubel_, Jun 11 2024

%K nonn

%O 1,1

%A _Cino Hilliard_, Aug 22 2004