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Primes p such that the nearest integer to p * Pi is prime.
2

%I #15 Mar 02 2024 18:30:22

%S 13,17,31,53,71,73,101,181,197,223,229,239,241,281,311,313,353,367,

%T 491,521,607,821,859,863,919,1129,1217,1303,1381,1427,1471,1583,1667,

%U 1721,1723,1753,1811,1877,1879,1933,1979,2017,2063,2089,2221,2399,2441,2447

%N Primes p such that the nearest integer to p * Pi is prime.

%H Vincenzo Librandi, <a href="/A116671/b116671.txt">Table of n, a(n) for n = 1..1000</a>

%e floor (13Pi + .5) = 41.

%e floor (17Pi + .5) = 53.

%t lst={}; Do[p=Prime[n]; If[PrimeQ[Round[p*Pi]], AppendTo[lst,p]],{n,10^3}]; lst

%t Select[Prime[Range[400]],PrimeQ[Round[# Pi]]&] (* _Harvey P. Dale_, Mar 02 2024 *)

%K nonn,easy

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Aug 25 2008

%E Edited by _Charles R Greathouse IV_, Nov 11 2009