A153664 Numbers k such that the fractional part of (3/2)^k is greater than 1-(1/k).

1, 14, 163, 1256, 2677, 8093, 49304, 49305, 158643, 164000, 835999, 2242294, 2242295, 2242296, 3965133, 25380333, 92600006, 92600007, 92600008, 92600009, 92600010, 92600011, 99267816, 125040717, 125040718

Offset: 1

Author

Hieronymus Fischer, Dec 31 2008

Keywords

• nonn
• more

Comments

Numbers k such that fract((3/2)^k) > 1-(1/k), where fract(x) = x-floor(x).

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

Examples

			a(2) = 14 since fract((3/2)^14) = 0.92926... > 0.92857... = 1 - (1/14), but fract((3/2)^k) <= 1 - (1/k) for 1<k<14.
		

Crossrefs

Cf. A002379, A081464, A153662, A153663, A153665, A153666, A153667, A153668.

Programs

Mathematica

Select[Range[1000], FractionalPart[(3/2)^#] >= 1 - (1/#) &] (* G. C. Greubel, Aug 24 2016 *)

Extensions

a(11)-a(25) from Robert Gerbicz, Nov 21 2010