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

1,2

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

Links

Table of n, a(n) for n=1..16.

Example

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A217688 A263570 A029733 * A042137 A067976 A154316

Adjacent sequences: A153683 A153684 A153685 * A153687 A153688 A153689

Keyword

nonn,more

Author

Hieronymus Fischer, Jan 06 2009

Extensions

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

Status

approved