A247782 -id:A247782 - cp's OEIS frontend

A247781 Least k such that 1/e - (1 - 1/k)^k < 1/n.

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, 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, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15

Offset: 1

Clark Kimberling, Sep 24 2014

a(n+1) - a(n) is in {0,1} for n >= 1.

			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.

Clark Kimberling, Table of n, a(n) for n = 1..5000

Cf. A247782, A247783, A247778.

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*)

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

Original entry on oeis.org

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

Clark Kimberling, Sep 24 2014

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

			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.

Clark Kimberling, Table of n, a(n) for n = 1..900

Cf. A247781, A247782, A247789.

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*)

cp's OEIS Frontend

A247781 Least k such that 1/e - (1 - 1/k)^k < 1/n.

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