A153708
Greatest number m such that the fractional part of e^A153704(n) >= 1-(1/m).
Original entry on oeis.org
3, 23, 27, 261, 348, 2720, 72944, 347065, 244543
Offset: 1
a(2) = 23, since 1-(1/24) = 0.9583... > fract(e^A153704(2)) = fract(e^8) = 0.95798... >= 0.95652... >= 1-(1/23).
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A153704 = {1, 8, 19, 178, 209, 1907, 32653, 119136, 220010};
Table[fp = FractionalPart[E^A153704[[n]]]; m = Floor[1/fp];
While[fp >= 1 - (1/m), m++]; m - 1, {n, 1, Length[A153704]}] (* Robert Price, May 10 2019 *)
A153716
Greatest number m such that the fractional part of Pi^A153712(n) >= 1-(1/m).
Original entry on oeis.org
1, 7, 32, 53, 189, 131, 2665, 10810, 2693, 1976, 3697, 4289, 26577, 483367
Offset: 1
a(3) = 32, since 1-(1/33) = 0.9696... > fract(Pi^A153712(3)) = fract(Pi^15) = 0.96938... >= 0.96875 = 1-(1/32).
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A153712 = {1, 2, 15, 22, 58, 109, 157, 1030, 1071, 1274, 2008, 2322,
5269, 151710};
Table[Floor[1/(1 - FractionalPart[Pi^A153712[[n]]])], {n, 1,
Length[A153712]}] (* Robert Price, May 10 2019 *)
A153720
Numbers k such that the fractional part of (Pi-2)^k is greater than 1-(1/k).
Original entry on oeis.org
1, 5, 8, 85, 911, 2921, 4491, 11543, 15724, 27683, 29921, 37276, 126659
Offset: 1
a(3) = 8, since fract((Pi-2)^8) = 0.8846247315... > 0.875 = 1 - (1/8), but fract((Pi-2)^k) = 0.2134..., 0.5268... <= 1 - (1/k) for 6 <= k <= 7.
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Select[Range[1000], N[FractionalPart[(Pi - 2)^#], 100] > 1 - (1/#) &] (* G. C. Greubel, Aug 25 2016 *)
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).
A153676
Greatest number m such that the fractional part of (101/100)^A153672(n) >= 1-(1/m).
Original entry on oeis.org
1, 76, 238, 913, 1334, 4645, 17396, 351085, 69587, 552184, 329808, 381654, 35874097, 5011174, 6220178, 33773592, 13149134, 105749940
Offset: 1
a(2)=76, since 1-(1/77)=0.9870...>fract((101/100)^A153672(2))=fract((101/100)^69)=0.98689...>=1-(1/76).
Showing 1-7 of 7 results.
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