|
|
A153712
|
|
Numbers k such that the fractional part of Pi^k is greater than 1-(1/k).
|
|
9
|
|
|
1, 2, 15, 22, 58, 109, 157, 1030, 1071, 1274, 2008, 2322, 5269, 151710
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Numbers k such that fract(Pi^k) > 1-(1/k), where fract(x) = x-floor(x).
The next such number must be greater than 100000.
|
|
LINKS
|
|
|
EXAMPLE
|
a(3) = 15, since fract(Pi^15) = 0.969... > 0.933... = 1 - (1/15), but fract(Pi^k) <= 1 - (1/k) for 3 <= k <= 14.
|
|
MATHEMATICA
|
Select[Range[1000], N[FractionalPart[Pi^#], 100] > 1 - (1/#) &] (* G. C. Greubel, Aug 25 2016 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|