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