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%I #13 Mar 25 2015 00:22:07
%S 1,3,4,12,73,317,2728,6826,7683,7950,14417,44436,63698
%N Numbers n such that floor(Pi^n) is prime.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Pi-Prime.html">Pi-Prime</a>
%e Pi^3 =31.0062766...; floor(Pi^3) = 31 is prime, hence 3 is a term.
%e floor(Pi^317)=39492046894389575314518015275156522234256325244858662\
%e 9384386892199657951784561879730228789865483929643927422740165980523\
%e 92448365675861748301474339092198412631 is prime.
%t Do[ If[ PrimeQ[ Floor[ Pi^n ] ], Print[n] ], {n, 0, 4000} ]
%t $MaxExtraPrecision = 10^6; Do[k = Floor[Pi^n]; If[PrimeQ[k], Print[n]], {n, 1, 15000}] (* _Ryan Propper_ *)
%Y Cf. A100800, A077547.
%K hard,nonn
%O 1,2
%A _Naohiro Nomoto_, Feb 22 2001
%E More terms from _Vladeta Jovovic_, Feb 24 2001
%E One more term from _Robert G. Wilson v_, May 09 2001
%E a(8)-a(11) from _Ryan Propper_, Oct 21 2005
%E a(12)-a(13) from _Donovan Johnson_, Feb 05 2008
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