A154132 Minimal exponents m such that the fractional part of (4/3)^m increases monotonically (when starting with m=1).

1, 2, 8, 39, 2495, 3895, 4714, 8592

Offset: 1

Author

Hieronymus Fischer, Jan 11 2009

Keywords

• nonn
• more

Comments

Recursive definition: a(1)=1, a(n) = least number m>a(n-1) such that the fractional part of (4/3)^m is greater than the fractional part of (4/3)^k for all k, 1<=k

The next such number must be greater than 200000.

Examples

			a(4)=39, since fract((4/3)^39)= 0.999186..., but fract((4/3)^k)<0.9887... for 1<=k<=38; thus fract((4/3)^39)>fract((4/3)^k) for 1<=k<39 and 39 is the minimal exponent > 8 with this property.
		

Crossrefs

Cf. A153663, A153671, A091560, A153710, A154140, A154148.

Cf. A002379, A064628.

Formula

Recursion: a(1):=1, a(k):=min{ m>1 | fract((4/3)^m) > fract((4/3)^a(k-1))}, where fract(x) = x-floor(x).

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