A067559 -id:A067559 - cp's OEIS frontend

A062408 Numbers k such that floor(Pi*k) is prime.

1, 10, 12, 14, 15, 17, 19, 31, 33, 35, 36, 42, 50, 52, 57, 61, 63, 71, 73, 77, 80, 82, 84, 98, 99, 101, 117, 119, 122, 124, 138, 140, 143, 147, 159, 166, 182, 187, 189, 201, 206, 208, 210, 220, 226, 229, 241, 245, 254, 262, 264, 273, 275, 289, 290, 296, 308, 311

Offset: 0

Jason Earls, Jul 08 2001

nonn

Chua, Park, & Smith prove a general result that implies that, for any m, there is a constant C(m) such that a(n+m) - a(n) < C(m) infinitely often. - Charles R Greathouse IV, Jun 30 2022

Harry J. Smith, Table of n, a(n) for n = 0..1000
Lynn Chua, Soohyun Park, and Geoffrey D. Smith, Bounded gaps between primes in special sequences, Proceedings of the AMS, Volume 143, Number 11 (November 2015), pp. 4597-4611.

Cf. A022844, A067559.

Select[Range[1, 400], PrimeQ[Floor[Pi #]] &] (* Bruno Berselli, Sep 30 2012 *)

je=[]; for(n=0,1000, if(isprime(floor(Pi*n)),je=concat(je,n),)); je

{ default(realprecision, 50); n=-1; for (m=1, 10^5, if (isprime(floor(Pi*m)), write("b062408.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 07 2009

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

Original entry on oeis.org

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

K. D. Bajpai, Sep 23 2013

nonn

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

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

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

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

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

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

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A062408 Numbers k such that floor(Pi*k) is prime.

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

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