A137994
a(n) is the smallest integer > a(n-1) such that {Pi^a(n)} < {Pi^a(n-1)}, where {x} = x - floor(x), a(1)=1.
Original entry on oeis.org
1, 3, 81, 264, 281, 472, 1147, 2081, 3207, 3592, 10479, 12128, 65875, 114791, 118885
Offset: 1
a(3)=81, since {Pi^81}=0.0037011283.., but {Pi^k}>=0.0062766802... for 1<=k<=80; thus {Pi^81}<{Pi^k} for 1<=k<81. - _Hieronymus Fischer_, Jan 06 2009
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$MaxExtraPrecision = 10000;
p = .999;
Select[Range[1, 5000],
If[FractionalPart[Pi^#] < p, p = FractionalPart[Pi^#]; True] &] (* Robert Price, Mar 12 2019 *)
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default(realprecision,10^4); print1(a=1); for(i=1,100, f=frac(Pi^a); until( frac(Pi^a++)
A153705
Greatest number m such that the fractional part of e^A153701(n) <= 1/m.
Original entry on oeis.org
1, 2, 11, 11, 23, 28, 69, 85, 115, 964, 1153, 1292, 1296, 1877, 34015, 156075, 952945
Offset: 1
a(3)=11 since 1/12 < fract(e^A153701(3)) = fract(e^3) = 0.0855... <= 1/11.
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A153701 = {1, 2, 3, 9, 29, 45, 75, 135, 219, 732, 1351, 3315, 4795,
4920, 5469, 28414, 37373};
Table[fp = FractionalPart[E^A153701[[n]]]; m = Floor[1/fp];
While[fp <= 1/m, m++]; m - 1, {n, 1, Length[A153701]}] (* Robert Price, Mar 25 2019 *)
A153697
Greatest number m such that the fractional part of (10/9)^A153693(n) <= 1/m.
Original entry on oeis.org
9, 11, 30, 82, 6131, 26735, 29430, 76172, 151439, 227416, 771341, 2712159, 4490404
Offset: 1
a(2)=11 since 1/12 < fract((10/9)^A153693(2)) = fract((10/9)^7) = 0.09075... <= 1/11.
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A153693 = {1, 7, 50, 62, 324, 3566, 66877, 108201, 123956, 132891,
182098, 566593, 3501843};
Table[fp = FractionalPart[(10/9)^A153693[[n]]]; m = Floor[1/fp];
While[fp <= 1/m, m++]; m - 1, {n, 1, Length[A153693]}] (* Robert Price, Mar 25 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 1-6 of 6 results.
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