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.
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).
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