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 A153695 Minimal exponents m such that the fractional part of (10/9)^m obtains a maximum (when starting with m=1). 10
 1, 2, 3, 4, 5, 6, 13, 17, 413, 555, 2739, 3509, 3869, 5513, 12746, 31808, 76191, 126237, 430116, 477190, 1319307, 3596185 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. The next such number must be greater than 2*10^5. a(23) > 10^7. - Robert Price, Mar 24 2019 LINKS FORMULA 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). EXAMPLE 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. MATHEMATICA \$MaxExtraPrecision = 100000; p = 0; Select[Range[1, 20000], If[FractionalPart[(10/9)^#] > p, p = FractionalPart[(10/9)^#]; True] &] (* Robert Price, Mar 24 2019 *) PROG (Python) A153695_list, m, m10, m9, q = [], 1, 10, 9, 0 while m < 10**4:     r = m10 % m9     if r > q:         q = r         A153695_list.append(m)     m += 1     m10 *= 10     m9 *= 9     q *= 9 # Chai Wah Wu, May 16 2020 CROSSREFS Cf. A153663, A153671, A153679, A153687, A153699, A154130, A091560, A153711, A153719. Sequence in context: A223938 A222194 A057224 * A300857 A255261 A181303 Adjacent sequences:  A153692 A153693 A153694 * A153696 A153697 A153698 KEYWORD nonn,more AUTHOR Hieronymus Fischer, Jan 06 2009 EXTENSIONS a(19)-a(22) from Robert Price, Mar 24 2019 STATUS approved

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Last modified July 26 10:21 EDT 2021. Contains 346294 sequences. (Running on oeis4.)