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

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, 32, 33, 34, 36, 37, 38, 39, 40, 42, 43, 44, 45, 47, 48, 49, 50, 51, 53, 54, 55, 56, 58, 59, 60, 61, 63, 64, 65, 66, 67, 69, 70, 71, 72, 74, 75, 76, 77, 78, 80, 81

Offset

1,2

Comments

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

Links

Clark Kimberling, Table of n, a(n) for n = 1..4000

Example

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 six terms of A247782 are 1,3,4,5,6,7.

Mathematica

z = 400; f[n_] := f[n] = Select[Range[z], 1/E - (1 - 1/#)^# < 1/n &, 1];
u = Flatten[Table[f[n], {n, 1, z}]] (*A247781*)
d1 = Flatten[Position[Differences[u], 0]] (*A247782*)
d2 = Flatten[Position[Differences[u], 1]] (*A247783*)

Crossrefs

Cf. A247781, A247783, A247788.

Sequence in context: A155854 A047252 A039235 * A039179 A247914 A184518

Adjacent sequences: A247779 A247780 A247781 * A247783 A247784 A247785

Keyword

nonn,easy

Author

Clark Kimberling, Sep 24 2014

Status

approved