This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A137994 #25 Sep 27 2024 05:44:30
%S A137994 1,3,81,264,281,472,1147,2081,3207,3592,10479,12128,65875,114791,
%T A137994 118885
%N A137994 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 A137994 The sequence was suggested by _Leroy Quet_ on Pi day 2008, cf. A138324.
%C A137994 The next such number must be greater than 100000. - _Hieronymus Fischer_, Jan 06 2009
%C A137994 a(16) > 300,000. - _Robert Price_, Mar 25 2019
%e A137994 a(3)=81, since {Pi^81}=0.0037011283.., but {Pi^k}>=0.0062766802... for 1<=k<=80; thus {Pi^81}<{Pi^k} for 1<=k<81. - _Hieronymus Fischer_, Jan 06 2009
%t A137994 $MaxExtraPrecision = 10000;
%t A137994 p = .999;
%t A137994 Select[Range[1, 5000],
%t A137994 If[FractionalPart[Pi^#] < p, p = FractionalPart[Pi^#]; True] &] (* _Robert Price_, Mar 12 2019 *)
%o A137994 (PARI) default(realprecision,10^4); print1(a=1); for(i=1,100, f=frac(Pi^a); until( frac(Pi^a++)<f,); print1(","a))
%Y A137994 Cf. A001203, A138324, A001672.
%Y A137994 Cf. A081464, A153669, A153677, A153685, A153693, A153705, A153713, A154130, A153717. - _Hieronymus Fischer_, Jan 06 2009
%K A137994 nonn,more,hard
%O A137994 1,2
%A A137994 _Leroy Quet_ and _M. F. Hasler_, Mar 14 2008
%E A137994 a(11)-a(13) from _Hieronymus Fischer_, Jan 06 2009
%E A137994 Edited by _R. J. Mathar_, May 21 2010
%E A137994 a(14)-a(15) from _Robert Price_, Mar 12 2019