A153672 Numbers k such that the fractional part of (101/100)^k is greater than 1-(1/k).

1, 69, 180, 783, 859, 1803, 10763, 19105, 39568, 50172, 132572, 355146, 1452050, 2245950, 3047334, 3933030, 4165171, 98544173

Offset: 1

Author

Hieronymus Fischer, Jan 06 2009

Keywords

• nonn
• more

Comments

Numbers k such that fract((101/100)^k) > 1-(1/k), where fract(x) = x-floor(x).

The next term is greater than 2*10^8.

Examples

			a(2) = 69, since fract((101/100)^69) = 0.9868... > 0.9855... = 1 - (1/69), but fract((101/100)^k) <= 1 - (1/k) for 1 < k < 69.
		

Crossrefs

Cf. A153664, A154130, A153676, A153680, A153688, A153696, A153704, A153712, A153720.

Programs

Mathematica

Select[Range[1000], FractionalPart[(101/100)^#] >= 1 - (1/#) &] (* G. C. Greubel, Aug 24 2016 *)

Extensions

a(13)-a(18) from Robert Gerbicz, Nov 22 2010