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 A211705 #16 Jun 09 2024 22:01:28
%S A211705 3,2,1,3,3,9,0,3,0,4,8,3,0,5,8,3,5,2,7,5,6,6,6,0,3,0,4,6,3,8,1,8,4,9,
%T A211705 1,6,0,9,6,1,1,5,9,3,4,3,0,1,1,5,1,2,8,7,1,5,5,6,1,5,9,1,0,7,3,8,2,8,
%U A211705 3,6,8,4,1,4,8,6,9,7,3,3,8,1,1,3,1,4,2
%N A211705 Decimal expansion of Sum_{n>=1} A006218(n)*2^(-n).
%F A211705 Equals 2 * A065442. - _Amiram Eldar_, Aug 01 2020
%e A211705 Sum_{n>=1} A006218(n)*2^(-n) = 1/2 + 3/4 + 5/8 + 8/16 + 10/32 + 14/64 + ... = 3.213390304830583527566603046381849...
%t A211705 f[n_, m_] := Sum[Floor[n/k], {k, 1, m}]
%t A211705 t = Table[f[n, 100], {n, 1, 4000}] ;
%t A211705 N[Sum[t[[n]]/2^n, {n, 1, 4000}], 100]
%t A211705 RealDigits[%, 10] (* A211705 *)
%t A211705 RealDigits[%%, 2] (* A211706 *)
%o A211705 (PARI) k=1.; 2*suminf(n=1, k>>=1; k^n*(1+k)/(1-k)) \\ _Charles R Greathouse IV_, Jul 18 2021
%Y A211705 Cf. A006218, A065442, A211701, A211706 (binary).
%K A211705 nonn,cons
%O A211705 1,1
%A A211705 _Clark Kimberling_, Apr 19 2012
%E A211705 a(31) onward corrected by _Sean A. Irvine_, Jun 09 2024