A247988 Least number k such that e - k/(k!)^(1/k) < 1/n.

4, 11, 19, 27, 36, 45, 54, 64, 74, 84, 94, 105, 115, 126, 136, 147, 158, 169, 180, 191, 203, 214, 225, 237, 248, 260, 272, 283, 295, 307, 319, 331, 343, 355, 367, 379, 391, 403, 416, 428, 440, 452, 465, 477, 490, 502, 515, 527, 540, 552, 565, 578, 590, 603

Offset: 1

Author

Clark Kimberling, Sep 29 2014

Keywords

• nonn
• easy

Examples

			Let w(n) = e - n/(n!)^(1/n).  Approximations are shown here:
n .... w(n)  ...... 1/n
1 .... 1.71828 .... 1
2 .... 1.30407 .... 0.5
3 .... 1.06732 .... 0.333333
4 .... 0.911078 ... 0.25
5 .... 0.799022 ... 0.2
10 ... 0.510157 ... 0.1
11 ... 0.477609 ... 0.090909
a(2) = 11 because w(11) < 1/2 < w(10).
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 14.

Crossrefs

Cf. A247778, A247908, A247911, A247914, A247985.

Programs

Mathematica

$MaxExtraPrecision = Infinity;
z = 1000; p[k_] := p[k] = k/(k!)^(1/k) (* Finch p. 14 *)
N[Table[E - p[n], {n, 1, z}]];
f[n_] := f[n] = Select[Range[z], E - p[#] < 1/n &, 1];
u = Flatten[Table[f[n], {n, 1, z/10}]]  (* A247988 *)