cp's OEIS Frontend

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

%I A247988 #4 Sep 30 2014 15:57:21
%S A247988 4,11,19,27,36,45,54,64,74,84,94,105,115,126,136,147,158,169,180,191,
%T A247988 203,214,225,237,248,260,272,283,295,307,319,331,343,355,367,379,391,
%U A247988 403,416,428,440,452,465,477,490,502,515,527,540,552,565,578,590,603
%N A247988 Least number k such that e - k/(k!)^(1/k) < 1/n.
%D A247988 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 14.
%e A247988 Let w(n) = e - n/(n!)^(1/n).  Approximations are shown here:
%e A247988 n .... w(n)  ...... 1/n
%e A247988 1 .... 1.71828 .... 1
%e A247988 2 .... 1.30407 .... 0.5
%e A247988 3 .... 1.06732 .... 0.333333
%e A247988 4 .... 0.911078 ... 0.25
%e A247988 5 .... 0.799022 ... 0.2
%e A247988 10 ... 0.510157 ... 0.1
%e A247988 11 ... 0.477609 ... 0.090909
%e A247988 a(2) = 11 because w(11) < 1/2 < w(10).
%t A247988 $MaxExtraPrecision = Infinity;
%t A247988 z = 1000; p[k_] := p[k] = k/(k!)^(1/k) (* Finch p. 14 *)
%t A247988 N[Table[E - p[n], {n, 1, z}]];
%t A247988 f[n_] := f[n] = Select[Range[z], E - p[#] < 1/n &, 1];
%t A247988 u = Flatten[Table[f[n], {n, 1, z/10}]]  (* A247988 *)
%Y A247988 Cf. A247778, A247908, A247911, A247914, A247985.
%K A247988 nonn,easy
%O A247988 1,1
%A A247988 _Clark Kimberling_, Sep 29 2014