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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

%I #8 Mar 12 2014 15:12:45

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

%N 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.

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

%C At n=26974, the discrepancy from an integer is 0.00002313... - _Ryan Propper_, Jul 26 2005

%t $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 *)

%Y Cf. A079490, A080052, A080279-A080284.

%K more,nonn

%O 1,2

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

%E One more term from _Ryan Propper_, Jul 26 2005

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Last modified April 16 04:02 EDT 2024. Contains 371696 sequences. (Running on oeis4.)