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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

Table of n, a(n) for n=1..22.

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 *)

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 August 21 06:14 EDT 2019. Contains 326162 sequences. (Running on oeis4.)