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.
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).
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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