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A153686 Numbers k such that the fractional part of (11/10)^k is less than 1/k. 11
1, 2, 3, 17, 37, 48, 237, 420, 599, 615, 6638, 13885, 13886, 62963, 1063942, 9479731 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 28 09:54 EDT 2021. Contains 346326 sequences. (Running on oeis4.)