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 A082833 #25 Jan 16 2020 20:20:13
%S A082833 2,1,3,2,7,4,6,5,7,9,9,5,9,0,0,3,6,6,8,6,6,3,9,4,0,1,4,8,6,9,3,9,5,1,
%T A082833 2,8,4,3,7,5,0,9,5,1,7,0,3,2,7,0,0,2,1,8,1,7,2,5,1,1,8,9,5,4,1,9,7,7,
%U A082833 8,8,4,2,7,2,4,5,1,3,3,5,3,7,5,3,8,1,2,0,1,3,0,2,8,4,0,6,9,3,5,4,7,7,8,9,7
%N A082833 Decimal expansion of Kempner series Sum_{k >= 1, k has no digit 4 in base 10} 1/k.
%C A082833 Numbers with a digit 4 (A011534) 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 A082833 Julian Havil, Gamma, Exploring Euler's Constant, Princeton University Press, Princeton and Oxford, 2003, page 34.
%H A082833 Robert Baillie, <a href="http://www.jstor.org/stable/2321096">Sums of reciprocals of integers missing a given digit</a>, Amer. Math. Monthly, 86 (1979), 372-374.
%H A082833 Robert Baillie, <a href="http://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 A082833 Wikipedia, <a href="http://en.wikipedia.org/wiki/Kempner_series">Kempner series</a>. [From _M. F. Hasler_, Jan 13 2020]
%H A082833 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 A082833 Equals Sum_{k in A052406\{0}} 1/k, where A052406 = numbers with no digit 3. - _M. F. Hasler_, Jan 15 2020
%e A082833 21.32746579959003668663940148693951284375095170327002181725118954... - _Robert G. Wilson v_, Jun 01 2009
%t A082833 (* see the Mmca in Wolfram Library Archive *) (* _Robert G. Wilson v_, Jun 01 2009 *)
%o A082833 (PARI) sumpos(k=2,1/A052406(k)) \\ For illustration only, slow and not very precise: with \p19 takes 2 sec to get 5 digits right. - _M. F. Hasler_, Jan 13 2020
%Y A082833 Cf. A002387, A024101, A052406 (numbers with no 4), A011534 (numbers with a 4).
%Y A082833 Cf. A082830, A082831, A082832, A082834, A082835, A082836, A082837, A082838, A082839 (analog for digits 1, 2, ..., 9 and 0).
%K A082833 nonn,cons,base
%O A082833 2,1
%A A082833 _Robert G. Wilson v_, Apr 14 2003
%E A082833 More terms from _Robert G. Wilson v_, Jun 01 2009