A059792 Numbers n such that floor(Pi^n) is prime.

1, 3, 4, 12, 73, 317, 2728, 6826, 7683, 7950, 14417, 44436, 63698

Offset

1,2

Links

Table of n, a(n) for n=1..13.

Eric Weisstein's World of Mathematics, Pi-Prime

Example

Pi^3 =31.0062766...; floor(Pi^3) = 31 is prime, hence 3 is a term.
floor(Pi^317)=39492046894389575314518015275156522234256325244858662\
9384386892199657951784561879730228789865483929643927422740165980523\
92448365675861748301474339092198412631 is prime.

Mathematica

Do[ If[ PrimeQ[ Floor[ Pi^n ] ], Print[n] ], {n, 0, 4000} ]
$MaxExtraPrecision = 10^6; Do[k = Floor[Pi^n]; If[PrimeQ[k], Print[n]], {n, 1, 15000}] (* Ryan Propper *)

Crossrefs

Cf. A100800, A077547.

Sequence in context: A336687 A298115 A122903 * A018930 A127689 A307077

Adjacent sequences: A059789 A059790 A059791 * A059793 A059794 A059795

Keyword

hard,nonn

Author

Naohiro Nomoto, Feb 22 2001

Extensions

More terms from Vladeta Jovovic, Feb 24 2001

One more term from Robert G. Wilson v, May 09 2001

a(8)-a(11) from Ryan Propper, Oct 21 2005

a(12)-a(13) from Donovan Johnson, Feb 05 2008

Status

approved