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

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

Offset: 1

Author

Naohiro Nomoto, Feb 22 2001

Keywords

• hard
• nonn
• more
• changed

Examples

			Pi^3 = 31.0062766...; floor(Pi^3) = 31 is prime, hence 3 is a term.
		

Links

• Eric Weisstein's World of Mathematics, Pi-Prime

Crossrefs

Cf. A100800, A077547.

Programs

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, Oct 21 2005 *)

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