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A154133
Numbers k such that the fractional part of (4/3)^k is greater than 1-(1/k).
1
1, 2, 8, 39, 113, 3895, 4714, 8592, 34289, 60097, 942859, 2759790, 6649343, 7937397, 14480816, 19338413, 19338414, 19338415, 23187701, 124679421
OFFSET
1,2
COMMENTS
Numbers k such that fract((4/3)^k) > 1-(1/k), where fract(x) = x - floor(x).
The next term is greater than 3*10^8.
EXAMPLE
a(4) = 39, since fract((4/3)^39) = 0.9991861450... > 0.974358... = 1 - (1/39), but fract((4/3)^k) <= 1 - (1/k) for 8 < k < 39.
MATHEMATICA
Select[Range[5000], N[FractionalPart[(4/3)^#], 100] > 1 - (1/#) &] (* G. C. Greubel, Sep 02 2016 *)
PROG
(PARI) isok(n) = frac((4/3)^n) > 1 - 1/n; \\ Michel Marcus, Sep 03 2016
KEYWORD
nonn,more
AUTHOR
Hieronymus Fischer, Jan 11 2009
EXTENSIONS
a(11)-a(20) from Robert Gerbicz, Nov 21 2010
STATUS
approved