A153686 Numbers k such that the fractional part of (11/10)^k is less than 1/k.

1, 2, 3, 17, 37, 48, 237, 420, 599, 615, 6638, 13885, 13886, 62963, 1063942, 9479731

Offset: 1

Author

Hieronymus Fischer, Jan 06 2009

Keywords

• nonn
• more

Comments

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

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

a(17) > 10^7. - Robert Price, Mar 19 2019

Examples

			a(4) = 17 since fract((11/10)^17) = 0.05447... < 1/17, but fract((11/10)^k) >= 1/k for 4 <= k <= 16.
		

Crossrefs

Cf. A153662, A153670, A153682, A153678, A154130, A153694, A153702, A153710, A153718.

Programs

Mathematica

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

Python

A153686_list, k, k10, k11 =  [], 1, 10, 11
while k < 10**6:
    if (k11 % k10)*k < k10:
        A153686_list.append(k)
    k += 1
    k10 *= 10
    k11 *= 11 # Chai Wah Wu, Apr 01 2021

Extensions

a(15)-a(16) from Robert Price, Mar 19 2019