A153714
Greatest number m such that the fractional part of Pi^A153710(n) <= 1/m.
Original entry on oeis.org
7, 159, 50, 10, 21, 55, 117, 270, 307, 744, 757, 7804, 13876, 62099, 70718, 154755
Offset: 1
a(2)=159 since 1/160<fract(Pi^A153710(2))=fract(Pi^3)=0.0062766...<=1/159.
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A153710 = {1, 3, 5, 9, 10, 11, 59, 81, 264, 281, 472, 3592, 10479,
12128, 65875, 118885};
Table[fp = FractionalPart[Pi^A153710[[n]]]; m = Floor[1/fp];
While[fp <= 1/m, m++]; m - 1, {n, 1, Length[A153710]}] (* Robert Price, May 10 2019 *)
A153718
Numbers k such that the fractional part of (Pi-2)^k is less than 1/k.
Original entry on oeis.org
1, 2, 23, 24, 35, 41, 65, 182, 72506, 107346
Offset: 1
a(3)=23 since fract((Pi-2)^23) = 0.0260069... < 1/23, but fract((Pi-2)^k) >= 1/k for 3 <= k <= 22.
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Select[Range[1000], N[FractionalPart[(Pi - 2)^#], 100] < (1/#) &] (* G. C. Greubel, Aug 25 2016 *)
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lista(nn) = for (n=1, nn, default(realprecision, n); if (frac((Pi-2)^n) < 1/n, print1(n, ", "))); \\ Michel Marcus, Nov 16 2014
A153706
Greatest number m such that the fractional part of e^A153702(n) <= 1/m.
Original entry on oeis.org
1, 2, 11, 11, 964, 34015, 156075, 952945, 170942, 247768, 397506
Offset: 1
a(3) = 11 since 1/12 < fract(e^A153702(3)) = fract(e^3) = 0.0855... <= 1/11.
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.
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.
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.
Showing 1-7 of 7 results.
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