# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a153711
Showing 1-1 of 1

%I A153711 #17 Mar 25 2019 17:20:20
%S A153711 1,2,15,22,58,157,1030,5269,145048,151710
%N A153711 Minimal exponents m such that the fractional part of Pi^m obtains a maximum (when starting with m=1).
%C A153711 Recursive definition: a(1)=1, a(n) = least number m>a(n-1) such that the fractional part of Pi^m is greater than the fractional part of Pi^k for all k, 1<=k<m.
%C A153711 The next such number must be greater than 100000.
%C A153711 a(11) > 300000. - _Robert Price_, Mar 25 2019
%F A153711 Recursion: a(1):=1, a(k):=min{ m>1 | fract(Pi^m) > fract(Pi^a(k-1))}, where fract(x) = x-floor(x).
%e A153711 a(3)=15, since fract(Pi^15)= 0.9693879984..., but fract(Pi^k)<=0.8696... for 1<=k<=14; thus fract(Pi^15)>fract(Pi^k) for 1<=k<15 and 15 is the minimal exponent > 2 with this property.
%t A153711 $MaxExtraPrecision = 100000;
%t A153711 p = 0; Select[Range[1, 10000],
%t A153711 If[FractionalPart[Pi^#] > p, p = FractionalPart[Pi^#]; True] &] (* _Robert Price_, Mar 25 2019 *)
%Y A153711 Cf. A153663, A153671, A153679, A153687, A153695, A153707, A153715, A154130, A153719.
%Y A153711 Cf. A001672.
%K A153711 nonn,more
%O A153711 1,2
%A A153711 _Hieronymus Fischer_, Jan 06 2009
%E A153711 a(9)-a(10) from _Robert Price_, Mar 25 2019

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE