A227794 Primes of the form: floor(Pi*n^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

1,1

Links

K. D. Bajpai, Table of n, a(n) for n = 1..1500

Example

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

Maple

KD:= proc() local a; a:=floor(evalf( Pi*n^2));  if isprime(a) then   RETURN(a): fi; end: seq(KD(), n=1..1000);

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A341047 A080174 A065117 * A225334 A240441 A229929

Adjacent sequences: A227791 A227792 A227793 * A227795 A227796 A227797

Keyword

nonn

Author

K. D. Bajpai, Sep 23 2013

Status

approved