A247783 Numbers k for which A247781(k+1) = 1+A247781(k).

2, 8, 13, 19, 24, 30, 35, 41, 46, 52, 57, 62, 68, 73, 79, 84, 90, 95, 101, 106, 111, 117, 122, 128, 133, 139, 144, 149, 155, 160, 166, 171, 177, 182, 188, 193, 198, 204, 209, 215, 220, 226, 231, 236, 242, 247, 253, 258, 264, 269, 274, 280, 285, 291, 296, 302

Offset

1,1

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..900

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 two terms of A247783 are 2, 8.

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, A247782, A247789.

Sequence in context: A304801 A184519 A156245 * A096274 A305879 A271383

Adjacent sequences: A247780 A247781 A247782 * A247784 A247785 A247786

Keyword

nonn,easy

Author

Clark Kimberling, Sep 24 2014

Status

approved