cp's OEIS Frontend

A153669 Minimal exponents m such that the fractional part of (101/100)^m obtains a minimum (when starting with m=1).

%I A153669 #14 Mar 21 2019 17:15:53
%S A153669 1,70,209,378,1653,2697,4806,13744,66919,67873,75666,81125,173389,
%T A153669 529938,1572706,4751419,7159431,7840546,15896994,71074288,119325567
%N A153669 Minimal exponents m such that the fractional part of (101/100)^m obtains a minimum (when starting with m=1).
%C A153669 Recursive definition: a(1)=1, a(n) = least number m>a(n-1) such that the fractional part of (101/100)^m is less than the fractional part of (101/100)^k for all k, 1<=k<m.
%C A153669 The next term is greater than 2*10^8.
%F A153669 Recursion: a(1):=1, a(k):=min{ m>1 | fract((101/100)^m) < fract((101/100)^a(k-1))}, where fract(x) = x-floor(x).
%e A153669 a(2)=70, since fract((101/100)^70)=0.00676..., but fract((101/100)^k)>=0.01 for 1<=k<=69; thus fract((101/100)^70)<fract((101/100)^k) for 1<=k<70.
%t A153669 p = 1; Select[Range[1, 5000],
%t A153669 If[FractionalPart[(101/100)^#] < p, p = FractionalPart[(101/100)^#];
%t A153669 True] &] (* _Robert Price_, Mar 21 2019 *)
%Y A153669 Cf. A081464, A154130, A153673, A153677, A153685, A153693, A153701, A137994, A153717.
%K A153669 nonn,more
%O A153669 1,2
%A A153669 _Hieronymus Fischer_, Jan 06 2009
%E A153669 a(15)-a(21) from _Robert Gerbicz_, Nov 22 2010