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 A021085 #37 Jun 04 2021 22:08:13
%S A021085 0,1,2,3,4,5,6,7,9,0,1,2,3,4,5,6,7,9,0,1,2,3,4,5,6,7,9,0,1,2,3,4,5,6,
%T A021085 7,9,0,1,2,3,4,5,6,7,9,0,1,2,3,4,5,6,7,9,0,1,2,3,4,5,6,7,9,0,1,2,3,4,
%U A021085 5,6,7,9,0,1,2,3,4,5,6,7,9,0,1,2,3,4,5,6,7,9,0,1,2,3,4,5,6,7,9
%N A021085 Decimal expansion of 1/81.
%C A021085 The decimal expansion of Sum_{n>=1} floor(n * tanh(Pi))/10^n is the same as that of 1/81 for the first 268 decimal places [Borwein et al.]
%C A021085 Sqrt(999999999999999999) = 9*sqrt(12345679012345679). - _Ryohei Miyadera_, Ken Hirotomi, Hiroyuki Ozaki and Atushi Tanaka, Jan 16 2006
%D A021085 J. Borwein, D. Bailey and R. Girgensohn, Experimentation in Mathematics: Computational Paths to Discovery, Peters, Boston, 2004. See Sect. 1.4.
%H A021085 Jean-François Alcover, <a href="/A021085/a021085.txt">300 digits of Sum_{n>=1} floor(n*tanh(Pi))/10^n</a>
%H A021085 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,1).
%F A021085 Equals Sum_{k >= 1} (1/2^k)*(1/5^k)*k. - _Eric Desbiaux_, Mar 11 2009
%F A021085 G.f.: x*(1 + 2*x + 3*x^2 + 4*x^3 + 5*x^4 + 6*x^5 + 7*x^6 + 9*x^7)/(1 - x^9). - _Ilya Gutkovskiy_, Jun 21 2016
%F A021085 From _Stefano Spezia_, Jun 03 2021: (Start)
%F A021085 a(n) = a(n-9) for n > 8.
%F A021085 Equals (1/10)*Sum_{n>0} 1/A052268(n). (End)
%t A021085 Table[Mod[n, 9], {n, 0, 120}] /. 8 -> 9 (* or *)
%t A021085 PadLeft[First@ #, Abs@ Last@ # + Length@ First@ #] &@ RealDigits[N[1/81, 120]] (* _Michael De Vlieger_, Jun 21 2016 *)
%t A021085 PadRight[{},120,{0,1,2,3,4,5,6,7,9}](* _Harvey P. Dale_, Apr 07 2019 *)
%Y A021085 Cf. A052268.
%K A021085 nonn,easy,cons
%O A021085 0,3
%A A021085 _N. J. A. Sloane_