A153680 Numbers k such that the fractional part of (1024/1000)^k is greater than 1-(1/k).

1, 29, 82, 134, 277, 1306, 2036, 2349, 6393, 9389, 9816, 21689, 34477, 145984, 171954, 956357, 2746739

Offset: 1

Author

Hieronymus Fischer, Jan 06 2009

Keywords

• nonn
• more

Comments

Numbers k such that fract((1024/1000)^k) > 1-(1/k), where fract(x) = x-floor(x).

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

Examples

			a(2) = 29, since fract((1024/1000)^29) = 0.98929... > 0.9655... = 1 - (1/29), but fract((1024/1000)^k) <= 1 - (1/k) for 1 < k < 29.
		

Crossrefs

Cf. A153664, A153672, A153684, A154130, A153688, A153696, A153704, A153712, A153720.

Programs

Mathematica

Select[Range[1000], FractionalPart[(1024/1000)^#] >= 1 - (1/#) &] (* G. C. Greubel, Aug 24 2016 *)

Extensions

a(16)-a(17) from Hagen von Eitzen, May 16 2009