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.
Original entry on oeis.org
1, 4, 10, 12, 20, 263, 964, 1533, 26974
Offset: 1
Mark Hudson (mrmarkhudson(AT)hotmail.com), Feb 13 2003
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$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 *)
A387495
Exponents k such that exp(k)/Pi is closer to an integer than for any smaller k.
Original entry on oeis.org
0, 1, 7, 22, 30, 50, 79, 103, 262, 993, 20819, 39397
Offset: 1
a(1) = 0: exp(0)/Pi = 0.3183... = distance to nearest integer 0;
a(2) = 1: exp(1)/Pi = 0.8652559..., distance to nearest integer 1 = 0.134744...;
a(3) = 7: exp(7)/Pi = 349.0691758..., distance to nearest integer 349 = 0.0691758...;
a(4) = 22: exp(22)/Pi = 1141113200.0309559..., distance to nearest integer = 0.0309...
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