This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A247911 #4 Sep 27 2014 19:02:50
%S A247911 1,2,2,3,3,4,5,5,6,6,7,8,8,9,10,10,11,11,12,13,13,14,14,15,16,16,17,
%T A247911 17,18,19,19,20,20,21,22,22,23,23,24,25,25,26,26,27,28,28,29,29,30,31,
%U A247911 31,32,32,33,34,34,35,35,36,37,37,38,38,39,39,40,41,41
%N A247911 Least number k such that (2*k+1)/u(2*k+1) - e < 1/n^n, where u is defined as in Comments.
%C A247911 The sequence u is define recursively by u(n) = u(n-1) + u(n-2)/(n-2), with u(1) = 0 and u(2) = 1. Let d(n) = a(n+1) - a(n). It appears that d(n) is in {2,3} for n >= 1, that d(n+1) - d(n) is in {-1,0,1}, and that similar bounds hold for higher differences.
%D A247911 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 19.
%H A247911 Clark Kimberling, <a href="/A247911/b247911.txt">Table of n, a(n) for n = 1..1000</a>
%e A247911 Approximations for the first few terms (2*n+1)/u(2*n+1) - e and 1/n^n are shown here:
%e A247911 n ... (2*n+1)/u(2*n+1)-e .. 1/n^n
%e A247911 1 ... 0.28171817 .......... 1
%e A247911 2 ... 0.0089908988 ........ 0.25
%e A247911 3 ... 0.0001647734 ........ 0.037037
%e A247911 4 ... 0.0000018654 ........ 0.00390625
%e A247911 5 ... 0.0000000143 ........ 0.00032000
%e A247911 a(2) = 2 because 5/u(5) - e < 1/3^3 < 3/u(3).
%t A247911 $RecursionLimit = 1000; $MaxExtraPrecision = 1000;
%t A247911 z = 300; u[1] = 0; u[2] = 1; u[n_] := u[n] = u[n - 1] + u[n - 2]/(n - 2);
%t A247911 f[n_] := f[n] = Select[Range[z], (2 # + 1)/u[2 # + 1] - E < n^-n &, 1];
%t A247911 u = Flatten[Table[f[n], {n, 1, z}]] (* A247911 *)
%t A247911 w = Differences[u]
%t A247911 Flatten[Position[w, 0]] (* A247912 *)
%t A247911 Flatten[Position[w, 1]] (* A247913 *)
%Y A247911 Cf. A247908, A247912, A247913, A247914.
%K A247911 nonn,easy
%O A247911 1,2
%A A247911 _Clark Kimberling_, Sep 27 2014