A153678 Numbers k such that the fractional part of (1024/1000)^k is less than 1/k.

1, 2, 3, 4, 5, 6, 585, 1164, 1707, 522271, 3675376, 3906074, 9424094

Offset: 1

Author

Hieronymus Fischer, Jan 06 2009

Keywords

• nonn
• more

Comments

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

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

a(14) > 10^7. - Robert Price, Mar 16 2019

Examples

			a(7) = 585 since fract((1024/1000)^585) = 0.00139... < 1/585, but fract((1024/1000)^k) >= 1/k for 7 <= k <= 584.
		

Crossrefs

Cf. A153662, A153670, A153682, A154130, A153686, A153694, A153702, A153710, A153718.

Programs

Mathematica

Select[Range[2000], FractionalPart[(1024/1000)^#] < (1/#) &] (* G. C. Greubel, Aug 24 2016; corrected by Robert Price, Mar 16 2019 *)

PARI

isok(n) = frac((1024/1000)^n) < 1/n \\ Michel Marcus, Aug 06 2013

Extensions

a(10)-a(13) from Robert Price, Mar 16 2019