A153684
Greatest number m such that the fractional part of (1024/1000)^A153680(n) >= 1-(1/m).
Original entry on oeis.org
1, 93, 123, 1061, 395, 1360, 4137, 2706, 66910, 21740, 15986, 58999, 571666, 1192010, 793642, 1093343, 3476524
Offset: 1
a(2)=93, since 1-(1/94)=0.98936...>fract((1024/1000)^A153680(2))=fract((1024/1000)^29)=0.98929...>=1-(1/93).
A153700
Greatest number m such that the fractional part of (10/9)^A153696(n) >= 1-(1/m).
Original entry on oeis.org
1, 8, 15, 264, 8741, 15912, 409895
Offset: 1
a(3)=15, since 1-(1/16)=0.9375>fract((10/9)^A153696(3))=fract((10/9)^13)=0.9341...>=1-(1/15).
A153692
Greatest number m such that the fractional part of (11/10)^A153688(n) >= 1-(1/m).
Original entry on oeis.org
1, 19, 151, 200, 709, 5727, 15908, 162819, 120479, 109526, 302991
Offset: 1
a(2)=19, since 1-(1/20)=0.95>fract((11/10)^A153688(2))=fract((11/10)^7)=0.9487...>=1-(1/19).
A154133
Numbers k such that the fractional part of (4/3)^k is greater than 1-(1/k).
Original entry on oeis.org
1, 2, 8, 39, 113, 3895, 4714, 8592, 34289, 60097, 942859, 2759790, 6649343, 7937397, 14480816, 19338413, 19338414, 19338415, 23187701, 124679421
Offset: 1
a(4) = 39, since fract((4/3)^39) = 0.9991861450... > 0.974358... = 1 - (1/39), but fract((4/3)^k) <= 1 - (1/k) for 8 < k < 39.
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Select[Range[5000], N[FractionalPart[(4/3)^#], 100] > 1 - (1/#) &] (* G. C. Greubel, Sep 02 2016 *)
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isok(n) = frac((4/3)^n) > 1 - 1/n; \\ Michel Marcus, Sep 03 2016
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