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%I #21 Mar 25 2019 12:11:42
%S 1,3,81,264,281,472,1147,2081,3207,3592,10479,12128,65875,114791,
%T 118885
%N a(n) is the smallest integer > a(n-1) such that {Pi^a(n)} < {Pi^a(n-1)}, where {x} = x - floor(x), a(1)=1.
%C The sequence was suggested by _Leroy Quet_ on Pi day 2008, cf. A138324.
%C The next such number must be greater than 100000. [_Hieronymus Fischer_, Jan 06 2009]
%C a(16) > 300,000. - _Robert Price_, Mar 25 2019
%e a(3)=81, since fract((Pi^81)=0.0037011283.., but fract(Pi^k)>=0.0062766802... for 1<=k<=80; thus fract(Pi^81)<fract(Pi^k) for 1<=k<81. [_Hieronymus Fischer_, Jan 06 2009]
%t $MaxExtraPrecision = 10000;
%t p = .999;
%t Select[Range[1, 5000],
%t If[FractionalPart[Pi^#] < p, p = FractionalPart[Pi^#]; True] &] (* _Robert Price_, Mar 12 2019 *)
%o (PARI) default(realprecision,10^4); print1(a=1); for(i=1,100, f=frac(Pi^a); until( frac(Pi^a++)<f,); print1(","a))
%Y Cf. A001203, A138324, A001672.
%Y Cf. A081464, A153669, A153677, A153685, A153693, A153705, A153713, A154130, A153717 [_Hieronymus Fischer_, Jan 06 2009]
%K nonn,more
%O 1,2
%A _Leroy Quet_ and _M. F. Hasler_, Mar 14 2008
%E a(11)-a(13) from _Hieronymus Fischer_, Jan 06 2009
%E Edited by _R. J. Mathar_, May 21 2010
%E a(14)-a(15) from _Robert Price_, Mar 12 2019
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