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 A153693 Minimal exponents m such that the fractional part of (10/9)^m obtains a minimum (when starting with m=1). 10
 1, 7, 50, 62, 324, 3566, 66877, 108201, 123956, 132891, 182098, 566593, 3501843 (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 less 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(14) > 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(2)=7, since fract((10/9)^7) = 0.09075.., but fract((10/9)^k) >= 0.11... for 1 <= k <= 6; thus fract((10/9)^7) < fract((10/9)^k) for 1 <= k < 7. MATHEMATICA \$MaxExtraPrecision = 100000; p = 1; Select[Range[1, 10000], If[FractionalPart[(10/9)^#] < p, p = FractionalPart[(10/9)^#]; True] &] (* Robert Price, Mar 24 2019 *) CROSSREFS Cf. A081464, A153669, A153677, A153685, A153697, A154130, A153701, A137994, A153717. Sequence in context: A067214 A069032 A271623 * A293475 A293801 A227676 Adjacent sequences:  A153690 A153691 A153692 * A153694 A153695 A153696 KEYWORD nonn,more AUTHOR Hieronymus Fischer, Jan 06 2009 EXTENSIONS a(12)-a(13) from Robert Price, Mar 24 2019 STATUS approved

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Last modified June 25 10:09 EDT 2021. Contains 345453 sequences. (Running on oeis4.)