cp's OEIS Frontend

A153695 Minimal exponents m such that the fractional part of (10/9)^m obtains a maximum (when starting with m=1).

%I A153695 #19 May 16 2020 12:40:01
%S A153695 1,2,3,4,5,6,13,17,413,555,2739,3509,3869,5513,12746,31808,76191,
%T A153695 126237,430116,477190,1319307,3596185
%N A153695 Minimal exponents m such that the fractional part of (10/9)^m obtains a maximum (when starting with m=1).
%C A153695 Recursive definition: a(1)=1, a(n) = least number m > a(n-1) such that the fractional part of (10/9)^m is greater than the fractional part of (10/9)^k for all k, 1 <= k < m.
%C A153695 The next such number must be greater than 2*10^5.
%C A153695 a(23) > 10^7. - _Robert Price_, Mar 24 2019
%F A153695 Recursion: a(1):=1, a(k):=min{ m>1 | fract((10/9)^m) > fract((10/9)^a(k-1))}, where fract(x) = x-floor(x).
%e A153695 a(7)=13, since fract((10/9)^13) = 0.93..., but fract((10/9)^k) < 0.89 for 1 <= k <= 12; thus fract((10/9)^13) > fract((10/9)^k) for 1 <= k < 13 and 13 is the minimal exponent > 6 with this property.
%t A153695 $MaxExtraPrecision = 100000;
%t A153695 p = 0; Select[Range[1, 20000],
%t A153695 If[FractionalPart[(10/9)^#] > p, p = FractionalPart[(10/9)^#];
%t A153695 True] &] (* _Robert Price_, Mar 24 2019 *)
%o A153695 (Python)
%o A153695 A153695_list, m, m10, m9, q = [], 1, 10, 9, 0
%o A153695 while m < 10**4:
%o A153695     r = m10 % m9
%o A153695     if r > q:
%o A153695         q = r
%o A153695         A153695_list.append(m)
%o A153695     m += 1
%o A153695     m10 *= 10
%o A153695     m9 *= 9
%o A153695     q *= 9 # _Chai Wah Wu_, May 16 2020
%Y A153695 Cf. A153663, A153671, A153679, A153687, A153699, A154130, A091560, A153711, A153719.
%K A153695 nonn,more
%O A153695 1,2
%A A153695 _Hieronymus Fischer_, Jan 06 2009
%E A153695 a(19)-a(22) from _Robert Price_, Mar 24 2019