|
|
A153710
|
|
Numbers k such that the fractional part of Pi^k is less than 1/k.
|
|
9
|
|
|
1, 3, 5, 9, 10, 11, 59, 81, 264, 281, 472, 3592, 10479, 12128, 65875, 118885
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Numbers k such that fract(Pi^k) < 1/k, where fract(x) = x-floor(x).
The next such number must be greater than 100000.
|
|
LINKS
|
|
|
EXAMPLE
|
a(4) = 9 since fract(Pi^9) = 0.0993... < 1/9, but fract(Pi^k) = 0.3891..., 0.2932..., 0.5310... for 6 <= k <= 8, which all are greater than 1/k.
|
|
MATHEMATICA
|
Select[Range[1000], N[FractionalPart[Pi^#], 100] < (1/#) &] (* G. C. Greubel, Aug 25 2016 *)
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|