A153693 Minimal exponents m such that the fractional part of (10/9)^m obtains a minimum (when starting with m=1).

1, 7, 50, 62, 324, 3566, 66877, 108201, 123956, 132891, 182098, 566593, 3501843

Offset: 1

Author

Hieronymus Fischer, Jan 06 2009

Keywords

• nonn
• more

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

Examples

			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.
		

Crossrefs

Cf. A081464, A153669, A153677, A153685, A153697, A154130, A153701, A137994, A153717.

Programs

Mathematica

$MaxExtraPrecision = 100000;
p = 1; Select[Range[1, 10000],
If[FractionalPart[(10/9)^#] < p, p = FractionalPart[(10/9)^#];
True] &] (* Robert Price, Mar 24 2019 *)

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).

Extensions

a(12)-a(13) from Robert Price, Mar 24 2019