A153693
Minimal exponents m such that the fractional part of (10/9)^m obtains a minimum (when starting with m=1).
Original entry on oeis.org
1, 7, 50, 62, 324, 3566, 66877, 108201, 123956, 132891, 182098, 566593, 3501843
Offset: 1
a(2)=7, since fract((10/9)^7) = 0.09075.., but fract((10/9)^k) >= 0.11... for 1 <= k <= 6; thus fract((10/9)^7) < fract((10/9)^k) for 1 <= k < 7.
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$MaxExtraPrecision = 100000;
p = 1; Select[Range[1, 10000],
If[FractionalPart[(10/9)^#] < p, p = FractionalPart[(10/9)^#];
True] &] (* Robert Price, Mar 24 2019 *)
A153689
Greatest number m such that the fractional part of (11/10)^A153685(n) <= 1/m.
Original entry on oeis.org
10, 18, 253, 618, 6009, 6767, 21386, 697723, 4186162, 31102351
Offset: 1
a(2)=18 since 1/19 < fract((11/10)^A153685(2)) = fract((11/10)^17) = 0.0544... <= 1/18.
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A153685 = {1, 17, 37, 237, 599, 615, 6638, 13885, 1063942, 9479731};
Table[fp = FractionalPart[(11/10)^A153685[[n]]]; m = Floor[1/fp];
While[fp <= 1/m, m++]; m - 1, {n, 1, Length[A153685]}] (* Robert Price, Mar 25 2019 *)
A153673
Greatest number m such that the fractional part of (101/100)^A153669(n) <= 1/m.
Original entry on oeis.org
100, 147, 703, 932, 1172, 3389, 7089, 8767, 11155, 17457, 20810, 25355, 1129226, 1741049, 1960780, 2179637, 2859688, 11014240, 75249086, 132665447, 499298451
Offset: 1
a(2)=147 since 1/148<fract((101/100)^A153669(2))=fract((101/100)^70)=0.00676...<=1/147.
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A153669 = {1, 70, 209, 378, 1653, 2697, 4806, 13744, 66919, 67873,
75666, 81125, 173389, 529938, 1572706, 4751419, 7159431, 7840546,
15896994, 71074288, 119325567};
Table[fp = FractionalPart[(101/100)^A153669[[n]]]; m = Floor[1/fp];
While[fp <= 1/m, m++]; m - 1, {n, 1, Length[A153669]}] (* Robert Price, Mar 25 2019 *)
A153681
Greatest number m such that the fractional part of (1024/1000)^A153677(n) <= 1/m.
Original entry on oeis.org
41, 60, 76, 116, 233, 463, 718, 1350, 12472, 13733, 17428, 27955, 32276, 41155, 62437, 69643, 111085, 811799, 2656810, 11462221, 56414953
Offset: 1
a(2)=60 since 1/61 < fract((1024/1000)^A153677(2)) = fract((1024/1000)^68) = 0.0164... <= 1/60.
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A153677 = {1, 68, 142, 341, 395, 490, 585, 1164, 1707, 26366, 41358,
46074, 120805, 147332, 184259, 205661, 385710, 522271, 3418770,
3675376, 9424094};
Table[fp = FractionalPart[(1024/1000)^A153677[[n]]]; m = Floor[1/fp];
While[fp <= 1/m, m++]; m - 1, {n, 1, Length[A153677]}] (* Robert Price, Mar 25 2019 *)
Showing 1-4 of 4 results.
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