A227794 Primes of the form floor(Pi*k^2).

3, 113, 907, 3019, 3631, 5281, 6361, 7853, 8171, 11689, 14957, 16741, 17203, 20611, 33329, 36643, 38707, 63347, 68813, 96211, 115811, 126923, 128189, 129461, 169093, 172021, 234139, 241051, 248063, 301907, 319691, 340049, 367453, 380459, 382649, 387047, 448883

Offset: 1

Author

K. D. Bajpai, Sep 23 2013

Keywords

• nonn

Examples

			a(2)=113: Pi*6^2 = 113.09 and 113 is prime.
a(3)=907: Pi*17^2 = 907.92 and 907 is prime.
		

Links

• Georg Fischer, Table of n, a(n) for n = 1..1500 [first 162 terms from _K. D. Bajpai_]

Crossrefs

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

Programs

Maple

select(isprime, {seq(floor(Pi*n^2),n=1..1000)}); [corrected by Georg Fischer, Sep 27 2024]

Mathematica

Select[Floor[Pi*Range[400]^2],PrimeQ] (* Harvey P. Dale, Dec 18 2016 *)

PARI

is(n)=my(r=sqrtint((n+1)\Pi)); Pi*r^2>n && isprime(n) \\ Charles R Greathouse IV, Sep 23 2013