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A247782 Numbers k for which A247781(k+1) = A247781(k). 3

%I #4 Sep 26 2014 17:24:18

%S 1,3,4,5,6,7,9,10,11,12,14,15,16,17,18,20,21,22,23,25,26,27,28,29,31,

%T 32,33,34,36,37,38,39,40,42,43,44,45,47,48,49,50,51,53,54,55,56,58,59,

%U 60,61,63,64,65,66,67,69,70,71,72,74,75,76,77,78,80,81

%N Numbers k for which A247781(k+1) = A247781(k).

%C Every positive integer is in exactly one of the sequences A247782 and A247783.

%H Clark Kimberling, <a href="/A247782/b247782.txt">Table of n, a(n) for n = 1..4000</a>

%e The values of 1/e - (1 - 1/k)^k for n = 1..9 are approximately

%e 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, so that the first six terms of A247782 are 1,3,4,5,6,7.

%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. A247781, A247783, A247788.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Sep 24 2014

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Last modified February 28 08:11 EST 2024. Contains 370393 sequences. (Running on oeis4.)