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 A153663 #14 May 12 2024 18:11:11
%S A153663 1,5,8,10,12,14,46,58,105,157,163,455,1060,1256,2677,8093,28277,33327,
%T A153663 49304,158643,164000,835999,2242294,25380333,92600006
%N A153663 Minimal exponents m such that the fractional part of (3/2)^m reaches a maximum (when starting with m=1).
%C A153663 Recursive definition: a(1)=1, a(n) = least number m such that the fractional part of (3/2)^m is greater than the
%C A153663 fractional part of (3/2)^k for all k, 1<=k<m.
%C A153663 The fractional part of k=835999 is .999999 5 which is greater than (k-1)/k. The fractional part of k=2242294 is .999999 8 which is greater than (k-1)/k. The fractional part of k=25380333 is .999999 98 which is greater than (k-1)/k. The fractional part of k=92600006 is .999999 998 which is greater than (k-1)/k. So, all additional numbers in this sequence must be in A153664 and >3*10^8. - _Robert Price_, May 09 2012
%F A153663 Recursion: a(1):=1, a(k):=min{ m>1 | fract((3/2)^m) > fract((3/2)^a(k-1))}, where fract(x) = x-floor(x).
%e A153663 a(2)=5, since fract((3/2)^5)=0.59375, but fract((3/2)^k)=0.5, 0.25, 0.375, 0.0625 for 1<=k<=4; thus
%e A153663 fract((3/2)^5)>fract((3/2)^k) for 1<=k<5.
%t A153663 a[1] = 1; a[n_] := a[n] = For[m = a[n-1]+1, True, m++, f = FractionalPart[(3/2)^m]; If[AllTrue[Range[m-1], f > FractionalPart[(3/2)^#]&], Print[n, " ", m]; Return[m]]];
%t A153663 Array[a, 21] (* _Jean-François Alcover_, Feb 25 2019 *)
%Y A153663 Cf. A002379, A153661, A153662, A153664, A153665, A153666, A153667, A153668.
%K A153663 nonn,more
%O A153663 1,2
%A A153663 _Hieronymus Fischer_, Dec 31 2008
%E A153663 a(22)-a(25) from _Robert Price_, May 09 2012