A153696 Numbers k such that the fractional part of (10/9)^k is greater than 1-(1/k).

1, 6, 13, 17, 5513, 12746, 126237, 430116, 477190, 1295623, 1319307, 3596185, 6109350

Offset: 1

Author

Hieronymus Fischer, Jan 06 2009

Keywords

• nonn
• more

Comments

Numbers k such that fract((10/9)^k) > 1-(1/k), where fract(x) = x-floor(x).

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

a(14) > 10^7. - Robert Price, Mar 24 2019

Examples

			a(3) = 13, since fract((10/9)^13) = 0.9341... > 0.923... = 1 - (1/13), but fract((10/9)^k) <= 1 - (1/k) for 1 < k < 13.
		

Crossrefs

Cf. A153664, A153672, A153680, A153688, A153700, A154130, A153704, A153712, A153720.

Programs

Mathematica

Select[Range[1000], FractionalPart[(10/9)^#] >= 1 - (1/#) &] (* G. C. Greubel, Aug 24 2016 *)

Extensions

a(8)-a(13) from Hans Havermann, Apr 04 2016