A247783 - OEIS

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

%S 2,8,13,19,24,30,35,41,46,52,57,62,68,73,79,84,90,95,101,106,111,117,

%T 122,128,133,139,144,149,155,160,166,171,177,182,188,193,198,204,209,

%U 215,220,226,231,236,242,247,253,258,264,269,274,280,285,291,296,302

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

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

%H Clark Kimberling, <a href="/A247783/b247783.txt">Table of n, a(n) for n = 1..900</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, so that the first two terms of A247783 are 2, 8.

%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, A247782, A247789.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Sep 24 2014