A153698
Greatest number m such that the fractional part of (10/9)^A153694(n) <= 1/m.
Original entry on oeis.org
9, 4, 11, 82, 6131, 4549, 26735, 8620, 14923, 20328, 151439, 227416, 771341, 2712159, 2676962, 2409266, 4490404, 4041364
Offset: 1
a(3) = 11 since 1/12 < fract((10/9)^A153694(3)) = fract((10/9)^7) = 0.09075... <= 1/11.
A153682
Greatest number m such that the fractional part of (1024/1000)^A153678(n) <= 1/m.
Original entry on oeis.org
41, 20, 13, 10, 7, 6, 718, 1350, 12472, 811799, 11462221, 8698270, 56414953
Offset: 1
a(5) = 7 since 1/8 < fract((1024/1000)^A153678(5)) = fract((1024/1000)^5) = 0.12589... <= 1/7.
A153690
Greatest number m such that the fractional part of (11/10)^A153686(n) <= 1/m.
Original entry on oeis.org
10, 4, 3, 18, 253, 58, 618, 484, 6009, 6767, 21386, 697723, 634293, 189959, 4186162, 31102351
Offset: 1
a(4) = 18 since 1/19 < fract((11/10)^A153686(4)) = fract((11/10)^17) = 0.05447... <= 1/18.
A154131
Numbers n such that the fractional part of (4/3)^n is less than 1/n.
Original entry on oeis.org
1, 4, 17, 1738, 1739, 12863, 15705, 109705, 174894, 289047, 720429, 2087694, 2087695, 4475944, 6968999
Offset: 1
a(3)=17 since fract((4/3)^17) = 0.03273... < 1/17, but fract((4/3)^k) >= 1/k for 5 <= k <= 16.
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Select[Range[1000], N[FractionalPart[(4/3)^#], 100] < (1/#) &] (* G. C. Greubel, Sep 02 2016 *)
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isok(n) = frac((4/3)^n) < 1/n; \\ Michel Marcus, Sep 03 2016
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