A153685 Minimal exponents m such that the fractional part of (11/10)^m obtains a minimum (when starting with m=1).

1, 17, 37, 237, 599, 615, 6638, 13885, 1063942, 9479731

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 (11/10)^m is less than the fractional part of (11/10)^k for all k, 1<=k

The next such number must be greater than 2*10^5.

a(11) > 10^7. Robert Price, Mar 19 2019

Examples

			a(2)=17, since fract((11/10)^17)=0.05447.., but fract((11/10)^k)>=0.1 for 1<=k<=16; thus fract((11/10)^17)<fract((11/10)^k) for 1<=k<17.
		

Crossrefs

Cf. A081464, A153669, A153689, A153677, A154130, A153693, A153701, A137994, A153717.

Programs

Mathematica

p = 1; Select[Range[1, 50000],
 If[FractionalPart[(11/10)^#] < p, p = FractionalPart[(11/10)^#];
True] &] (* Robert Price, Mar 19 2019 *)

Formula

Recursion: a(1):=1, a(k):=min{ m>1 | fract((11/10)^m) < fract((11/10)^a(k-1))}, where fract(x) = x-floor(x).

Extensions

a(9)-a(10) from Robert Price, Mar 19 2019

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