A153688 Numbers k such that the fractional part of (11/10)^k is greater than 1-(1/k).

1, 7, 77, 103, 320, 1821, 2992, 15290, 88651, 88652, 180168, 410498, 548816, 672732

Offset: 1

Author

Hieronymus Fischer, Jan 06 2009

Keywords

• nonn
• more

Comments

Numbers k such that fract((11/10)^k) > 1-(1/k), where fract(x) = x-floor(x).

The next such number must be greater than 2*10^5.

a(15) > 10^7. Robert Price, Mar 19 2019

Examples

			a(2) = 7, since fract((11/10)^7) = 0.9487... > 0.8571... = 1 - (1/7), but fract((11/10)^k) <= 1 - (1/k) for 1 < k < 7.
		

Crossrefs

Cf. A153664, A153672, A153684, A153692, A154130, A153696, A153704, A153712, A153720.

Programs

Mathematica

Select[Range[1000], FractionalPart[(11/10)^#] >= 1 - (1/#) &] (* G. C. Greubel, Aug 24 2016 *)

Extensions

a(12)-a(14) from Robert Price, Mar 19 2019