A153678
Numbers k such that the fractional part of (1024/1000)^k is less than 1/k.
Original entry on oeis.org
1, 2, 3, 4, 5, 6, 585, 1164, 1707, 522271, 3675376, 3906074, 9424094
Offset: 1
a(7) = 585 since fract((1024/1000)^585) = 0.00139... < 1/585, but fract((1024/1000)^k) >= 1/k for 7 <= k <= 584.
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Select[Range[2000], FractionalPart[(1024/1000)^#] < (1/#) &] (* G. C. Greubel, Aug 24 2016; corrected by Robert Price, Mar 16 2019 *)
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isok(n) = frac((1024/1000)^n) < 1/n \\ Michel Marcus, Aug 06 2013
A153686
Numbers k such that the fractional part of (11/10)^k is less than 1/k.
Original entry on oeis.org
1, 2, 3, 17, 37, 48, 237, 420, 599, 615, 6638, 13885, 13886, 62963, 1063942, 9479731
Offset: 1
a(4) = 17 since fract((11/10)^17) = 0.05447... < 1/17, but fract((11/10)^k) >= 1/k for 4 <= k <= 16.
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Select[Range[1000], FractionalPart[(11/10)^#] < (1/#) &] (* G. C. Greubel, Aug 24 2016 *)
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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
A153674
Greatest number m such that the fractional part of (101/100)^A153670(n) <= 1/m.
Original entry on oeis.org
100, 49, 33, 24, 19, 16, 13, 12, 10, 147, 703, 676, 932, 3389, 7089, 1129226, 1741049, 1356464, 1960780, 11014240, 75249086, 28657625, 132665447, 499298451
Offset: 1
a(5) = 19 since 1/20 < fract((101/100)^A153670(5)) = fract((101/100)^5) = 0.0510... <= 1/19.
Showing 1-3 of 3 results.
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