login
A153718
Numbers k such that the fractional part of (Pi-2)^k is less than 1/k.
7
1, 2, 23, 24, 35, 41, 65, 182, 72506, 107346
OFFSET
1,2
COMMENTS
Numbers k such that fract((Pi-2)^k) < 1/k, where fract(x) = x-floor(x).
The next such number must be greater than 200000.
a(11) > 10^6. - Jon E. Schoenfield, Nov 15 2014
EXAMPLE
a(3)=23 since fract((Pi-2)^23) = 0.0260069... < 1/23, but fract((Pi-2)^k) >= 1/k for 3 <= k <= 22.
MATHEMATICA
Select[Range[1000], N[FractionalPart[(Pi - 2)^#], 100] < (1/#) &] (* G. C. Greubel, Aug 25 2016 *)
PROG
(PARI) lista(nn) = for (n=1, nn, default(realprecision, n); if (frac((Pi-2)^n) < 1/n, print1(n, ", "))); \\ Michel Marcus, Nov 16 2014
KEYWORD
nonn,more
AUTHOR
Hieronymus Fischer, Jan 06 2009
STATUS
approved