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%I #5 Sep 25 2014 21:16:20
%S 1,1,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,
%T 7,8,8,8,8,8,8,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,12,12,12,12,
%U 12,13,13,13,13,13,13,14,14,14,14,14,15,15,15
%N Least k such that 1/e - (1 - 1/k)^k < 1/n.
%C a(n+1) - a(n) is in {0,1} for n >= 1.
%H Clark Kimberling, <a href="/A247781/b247781.txt">Table of n, a(n) for n = 1..5000</a>
%e The values of 1/e - (1 - 1/k)^k for n = 1..9 are approximately 0.367879, 0.117879, 0.0715831, 0.0514732, 0.0401994, 0.0329815, 0.0279628, 0.0242705, 0.02144, from which we see that the first 9 terms of A247781 are 1, 1, 2, 2, 2, 2, 2, 2, 3.
%t z = 400; f[n_] := f[n] = Select[Range[z], 1/E - (1 - 1/#)^# < 1/n &, 1];
%t u = Flatten[Table[f[n], {n, 1, z}]] (*A247781*)
%t d1 = Flatten[Position[Differences[u], 0]] (*A247782*)
%t d2 = Flatten[Position[Differences[u], 1]] (*A247783*)
%Y Cf. A247782, A247783, A247778.
%K nonn,easy
%O 1,3
%A _Clark Kimberling_, Sep 24 2014
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