A227794 - OEIS

%I #30 Sep 27 2024 05:40:47

%S 3,113,907,3019,3631,5281,6361,7853,8171,11689,14957,16741,17203,

%T 20611,33329,36643,38707,63347,68813,96211,115811,126923,128189,

%U 129461,169093,172021,234139,241051,248063,301907,319691,340049,367453,380459,382649,387047,448883

%N Primes of the form floor(Pi*n^2).

%H Georg Fischer, <a href="/A227794/b227794.txt">Table of n, a(n) for n = 1..1500</a> [first 162 terms from _K. D. Bajpai_]

%e a(2)=113: Pi*6^2 = 113.09 and 113 is prime.

%e a(3)=907: Pi*17^2 = 907.92 and 907 is prime.

%p select(isprime, {seq(floor(Pi*n^2),n=1..1000)}); [corrected by _Georg Fischer_, Spe 27 2024]

%t Select[Floor[Pi*Range[400]^2],PrimeQ] (* _Harvey P. Dale_, Dec 18 2016 *)

%o (PARI) is(n)=my(r=sqrtint((n+1)\Pi)); Pi*r^2>n && isprime(n) \\ _Charles R Greathouse IV_, Sep 23 2013

%Y Cf. A066643 (floor(Pi*n^2)), A067559 (n that produce primes).

%K nonn

%O 1,1

%A _K. D. Bajpai_, Sep 23 2013