A080285 Numbers n such that [(Pi+e)/(Pi-e)]^n is closer to its nearest integer than any value of [(Pi+e)/(Pi-e)]^k for 1 <= k < n.

1, 4, 10, 12, 20, 263, 964, 1533, 26974

Offset: 1

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Feb 13 2003

Keywords

• more
• nonn

Comments

At n=1533, the discrepancy from an integer is 0.000043205...

At n=26974, the discrepancy from an integer is 0.00002313... - Ryan Propper, Jul 26 2005

Crossrefs

Cf. A079490, A080052, A080279-A080284.

Programs

Mathematica

$MaxExtraPrecision = 10^6; x = (Pi + E)/(Pi - E); b = 1; Do[a = Abs[N[Round[x^n] - x^n, 30]]; If[a < b, Print[n]; b = a], {n, 1, 30000}] (* Ryan Propper, Jul 26 2005 *)

Extensions

One more term from Ryan Propper, Jul 26 2005