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 A071529 #15 Sep 05 2020 07:46:00
%S A071529 0,0,1,1,1,4,7,7,12,5,8,10,23,18,25,14,18,17,14,24,22,22,35,15,21,30,
%T A071529 29,33,37,30,27,47,49,44,54,55,53,51,46,46,43,60,64,65,79,64,64,67,73,
%U A071529 66,79,68,60,76,86,85,85,83,86,74,90,84,93,106,90,85,98,107,88,104,86
%N A071529 Number of 1's among the elements of the simple continued fraction for (1+1/n)^n.
%C A071529 It seems that lim_{n->infinity} a(n)/A069887(n) = C = 0.41..., which is close to (log(4)-log(3))/log(2)=0.415..., the expected density of 1's (cf. measure theory of continued fractions).
%H A071529 Amiram Eldar, <a href="/A071529/b071529.txt">Table of n, a(n) for n = 1..10000</a>
%e A071529 (1+1/14)^14 has for continued fraction [2, 1, 1, 1, 2, 6, 1, 7, 1, 6, 2, 1, 4, 21, 1, 1, 7, 1, 1, 1, 3, 2, 7, 2, 7, 1, 2, 4, 1, 3, 2, 1, 1, 1, 5, 1, 2, 5, 1, 2] which contains 18 "1's" hence a(14)=18.
%t A071529 Table[Count[ContinuedFraction[(1+1/n)^n],1],{n,80}] (* _Harvey P. Dale_, Mar 11 2013 *)
%o A071529 (PARI) for(n=1,100,s=(1+1/n)^n; print1(sum(i=1,length(contfrac(s)),if(1-component(contfrac(s),i),0,1)),","))
%K A071529 easy,nonn
%O A071529 1,6
%A A071529 _Benoit Cloitre_, Jun 02 2002