A154131 Numbers n such that the fractional part of (4/3)^n is less than 1/n.

1, 4, 17, 1738, 1739, 12863, 15705, 109705, 174894, 289047, 720429, 2087694, 2087695, 4475944, 6968999

Offset: 1

Author

Hieronymus Fischer, Jan 11 2009

Keywords

• nonn
• more

Comments

Numbers n such that fract((4/3)^n) < 1/n, where fract(x) = x - floor(x).

The next term is greater than 3*10^8.

Examples

			a(3)=17 since fract((4/3)^17) = 0.03273... < 1/17, but fract((4/3)^k) >= 1/k for 5 <= k <= 16.
		

Crossrefs

Cf. A153662, A153670, A153702, A137994, A154139, A154147.

Cf. A002379, A064628.

Programs

Mathematica

Select[Range[1000], N[FractionalPart[(4/3)^#], 100] < (1/#) &] (* G. C. Greubel, Sep 02 2016 *)

PARI

isok(n) = frac((4/3)^n) < 1/n; \\ Michel Marcus, Sep 03 2016

Extensions

a(10)-a(15) from Robert Gerbicz, Nov 21 2010