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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
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
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
KEYWORD
nonn,more
AUTHOR
Hieronymus Fischer, Jan 06 2009
EXTENSIONS
a(15)-a(16) from Robert Price, Mar 19 2019
STATUS
approved