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 A082834 #23 Jan 16 2020 20:20:41
%S A082834 2,1,8,3,4,6,0,0,8,1,2,2,9,6,9,1,8,1,6,3,4,0,7,2,3,5,0,4,0,6,0,9,1,8,
%T A082834 2,7,1,7,8,4,6,5,6,7,5,1,5,0,1,3,9,1,8,2,9,1,6,7,9,3,5,9,1,8,4,2,5,0,
%U A082834 8,6,2,6,6,8,8,2,2,9,3,8,3,5,7,7,7,2,1,3,8,3,1,9,3,2,9,2,5,4,8,8,1,3,2,4,4
%N A082834 Decimal expansion of Kempner series Sum_{k>=1, k has no digit 5 in base 10} 1/k.
%C A082834 Numbers with a digit 5 (A011535) have asymptotic density 1, i.e., here almost all terms are removed from the harmonic series, which makes convergence less surprising. See A082839 (the analog for digit 0) for more information about such so-called Kempner series. - _M. F. Hasler_, Jan 13 2020
%D A082834 Julian Havil, Gamma, Exploring Euler's Constant, Princeton University Press, Princeton and Oxford, 2003, page 34.
%H A082834 Robert Baillie, <a href="https://www.jstor.org/stable/2321096">Sums of reciprocals of integers missing a given digit</a>, Amer. Math. Monthly, 86 (1979), 372-374.
%H A082834 Robert Baillie, <a href="https://arxiv.org/abs/0806.4410"> Summing the curious series of Kempner and Irwin</a> arXiv:0806.4410 [math.CA], 2008-2015. [From _Robert G. Wilson v_, Jun 01 2009]
%H A082834 Wikipedia, <a href="http://en.wikipedia.org/wiki/Kempner_series">Kempner series</a>. [From _M. F. Hasler_, Jan 13 2020]
%H A082834 Wolfram Library Archive, KempnerSums.nb (8.6 KB) - Mathematica Notebook, <a href="http://library.wolfram.com/infocenter/MathSource/7166/"> Summing Kempner's Curious (Slowly-Convergent) Series</a>. [From _Robert G. Wilson v_, Jun 01 2009]
%F A082834 Equals Sum_{k in A052413\{0}} 1/k, where A052413 = numbers with no digit 5. - _M. F. Hasler_, Jan 15 2020
%e A082834 21.83460081229691816340723504060918271784656751501391829167935918... - _Robert G. Wilson v_, Jun 01 2009
%t A082834 (* see the Mmca in Wolfram Library Archive. - _Robert G. Wilson v_, Jun 01 2009 *)
%Y A082834 Cf. A002387, A024101, A052413 (numbers with no '5'), A011535 (numbers with a '5').
%Y A082834 Cf. A082830, A082831, A082832, A082833, A082835, A082836, A082837, A082838, A082839 (analog for digits 1, 2, ..., 9 and 0).
%K A082834 nonn,cons,base
%O A082834 2,1
%A A082834 _Robert G. Wilson v_, Apr 14 2003
%E A082834 More terms from _Robert G. Wilson v_, Jun 01 2009
%E A082834 Minor edits by _M. F. Hasler_, Jan 13 2020