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 A065444 #38 Jul 30 2024 17:04:11
%S A065444 1,1,0,0,9,1,8,1,9,0,8,3,6,2,0,0,7,3,6,3,7,9,8,5,5,1,0,1,6,5,4,3,8,0,
%T A065444 0,4,3,2,0,3,4,5,4,3,9,7,8,7,3,2,8,1,6,5,6,3,5,9,8,9,0,2,2,0,7,3,4,3,
%U A065444 8,3,4,9,0,2,1,9,8,3,4,7,4,8,8,9,2,0,0,3,4,9,2,1,8,0,0,7,0,4,0,2,3,5
%N A065444 Decimal expansion of 9*Sum_{k>=1} 1/(10^k-1).
%C A065444 This constant is the infinite sum of the reciprocals of repunits, R_n, with n>0 (A002275). - _Enrique Pérez Herrero_, Dec 06 2009
%D A065444 Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 354-361.
%H A065444 Harry J. Smith, <a href="/A065444/b065444.txt">Table of n, a(n) for n=1..2000</a>
%H A065444 Steven R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/constant/dig/dig.html">Digital Search Tree Constants</a> [Broken link]
%H A065444 Steven R. Finch, <a href="http://web.archive.org/web/20010413214937/http://www.mathsoft.com:80/asolve/constant/dig/dig.html">Digital Search Tree Constants</a> [From the Wayback machine]
%F A065444 Equals 9 * Sum_{k>=1} (1+x^k)/(1-x^k) * x^(k^2) where x = 1/10. This allows fast computation for this and similar sequences (involving Sum_{k>=1} x^k/(1-x^k) for some x < 1 ). - _Joerg Arndt_, Apr 25 2016
%e A065444 1.10091819083620073637985510165438004320345439787328165635989...
%t A065444 RealDigits[9*N[ Sum[1/(10^k - 1), {k, 1, Infinity}], 120]] [[1]]
%t A065444 A065444=RealDigits[ Block[{$MaxExtraPrecision = 100}, N[9*Sum[(-1 + 10^i)^-1, {i, 1, Infinity}], 130]]][[1]] (* _Enrique Pérez Herrero_, Dec 06 2009 *)
%t A065444 First[RealDigits[9 (Log10[10/9] - QPolyGamma[0, 1, 1/10]/Log[10]), 10, 120]] (* _Jan Mangaldan_, Apr 25 2016 *)
%o A065444 (PARI) { default(realprecision, 2080); x=9*suminf(k=1, 1/(10^k - 1)); for (n=1, 2000, d=floor(x); x=(x-d)*10; write("b065444.txt", n, " ", d)) } \\ _Harry J. Smith_, Oct 19 2009
%Y A065444 Equals 9*A073668.
%Y A065444 Cf. A000042, A002275, A067617 (continued fraction).
%K A065444 nonn,cons
%O A065444 1,5
%A A065444 _N. J. A. Sloane_, Nov 18 2001
%E A065444 More terms from _John W. Layman_, Nov 19 2001
%E A065444 ...733 (50th digit) expanded to ...7328165 etc. by _Frank Ellermann_, Feb 23 2002