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URL: https://oeis.org/A153720

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A153720
Numbers k such that the fractional part of (Pi-2)^k is greater than 1-(1/k).
7
1, 5, 8, 85, 911, 2921, 4491, 11543, 15724, 27683, 29921, 37276, 126659
OFFSET
1,2
COMMENTS
Numbers k such that fract((Pi-2)^k) > 1-(1/k), where fract(x) = x-floor(x).
The next such number must be greater than 200000.
a(14) > 300000. - Robert Price, Mar 26 2019
EXAMPLE
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.
MATHEMATICA
Select[Range[1000], N[FractionalPart[(Pi - 2)^#], 100] > 1 - (1/#) &] (* G. C. Greubel, Aug 25 2016 *)
KEYWORD
nonn,more
AUTHOR
Hieronymus Fischer, Jan 06 2009
STATUS
approved