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).
A153680
Numbers k such that the fractional part of (1024/1000)^k is greater than 1-(1/k).
Original entry on oeis.org
1, 29, 82, 134, 277, 1306, 2036, 2349, 6393, 9389, 9816, 21689, 34477, 145984, 171954, 956357, 2746739
Offset: 1
a(2) = 29, since fract((1024/1000)^29) = 0.98929... > 0.9655... = 1 - (1/29), but fract((1024/1000)^k) <= 1 - (1/k) for 1 < k < 29.
A153688
Numbers k such that the fractional part of (11/10)^k is greater than 1-(1/k).
Original entry on oeis.org
1, 7, 77, 103, 320, 1821, 2992, 15290, 88651, 88652, 180168, 410498, 548816, 672732
Offset: 1
a(2) = 7, since fract((11/10)^7) = 0.9487... > 0.8571... = 1 - (1/7), but fract((11/10)^k) <= 1 - (1/k) for 1 < k < 7.
A153696
Numbers k such that the fractional part of (10/9)^k is greater than 1-(1/k).
Original entry on oeis.org
1, 6, 13, 17, 5513, 12746, 126237, 430116, 477190, 1295623, 1319307, 3596185, 6109350
Offset: 1
a(3) = 13, since fract((10/9)^13) = 0.9341... > 0.923... = 1 - (1/13), but fract((10/9)^k) <= 1 - (1/k) for 1 < k < 13.
A153704
Numbers k such that the fractional part of e^k is greater than 1-(1/k).
Original entry on oeis.org
1, 8, 19, 178, 209, 1907, 32653, 119136, 220010
Offset: 1
a(2)=8, since fract(e^8) = 0.957987... >0.875 = 1-(1/8), but fract(e^k) = 0.389..., 0.085..., 0.598..., 0.413..., 0.428..., 0.633... for 2<=k<=7 which all are less than 1-(1/k).
A153712
Numbers k such that the fractional part of Pi^k is greater than 1-(1/k).
Original entry on oeis.org
1, 2, 15, 22, 58, 109, 157, 1030, 1071, 1274, 2008, 2322, 5269, 151710
Offset: 1
a(3) = 15, since fract(Pi^15) = 0.969... > 0.933... = 1 - (1/15), but fract(Pi^k) <= 1 - (1/k) for 3 <= k <= 14.
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).
-
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 *)
A153724
Greatest number m such that the fractional part of (Pi-2)^A153720(n) >= 1-(1/m).
Original entry on oeis.org
1, 16, 8, 158, 946, 8786, 16159, 20188, 61392, 34039, 31425, 59154, 217556
Offset: 1
a(4)=158, since 1-(1/159) = 0.993710... > fract((Pi-2)^A153720(4)) = fract(Pi^85) = 0.993693... >= 0.993670... = 1-(1/158).
-
A153720 = {1, 5, 8, 85, 911, 2921, 4491, 11543, 15724, 27683, 29921,
37276, 126659};
Table[Floor[1/(1 - FractionalPart[(Pi - 2)^A153720[[n]]])], {n, 1,
Length[A153720]}] (* Robert Price, May 10 2019 *)
Showing 1-10 of 14 results.
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