A154130
Exponents m with decreasing fractional part of (4/3)^m.
Original entry on oeis.org
1, 4, 13, 17, 128, 485, 692, 1738, 12863, 77042, 109705, 289047, 720429, 4475944, 75629223, 182575231
Offset: 1
a(3)=13, since fract((4/3)^13)=0.0923.., but fract((4/3)^k)>=0.16... for 1<=k<=12; thus fract((4/3)^13)<fract((4/3)^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).
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).
A154137
Greatest number m such that the fractional part of (4/3)^A154133(n) >= 1-(1/m).
Original entry on oeis.org
1, 4, 88, 1228, 187, 4562, 8183, 167378, 35419, 77421, 5593723, 3306511, 83205705, 22413581, 24296709, 35457806, 26593355, 19945016, 80184972, 389460601
Offset: 1
a(3)=88, since 1-(1/89)=0.988764...>fract((4/3)^A154133(3))=fract((4/3)^8)=0.988721...>0.988636...=1-(1/88).
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