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 A082835 #26 Feb 16 2025 08:32:49
%S A082835 2,2,2,0,5,5,9,8,1,5,9,5,5,6,0,9,1,8,8,4,1,6,7,3,8,0,4,8,0,0,0,7,5,2,
%T A082835 7,1,0,5,1,9,3,8,5,6,1,0,6,6,6,8,4,6,3,2,7,0,2,7,6,9,3,8,2,3,3,0,5,3,
%U A082835 2,2,8,3,5,0,8,9,1,2,4,7,5,2,6,3,4,7,7,7,6,9,9,7,4,0,5,8,9,1,4,9,3,4,4,2,5
%N A082835 Decimal expansion of Kempner series Sum_{k >= 1, k has no digit 6 in base 10} 1/k.
%C A082835 Numbers with a digit 6 (A011536) 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 A082835 Julian Havil, Gamma, Exploring Euler's Constant, Princeton University Press, Princeton and Oxford, 2003, page 34.
%H A082835 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 A082835 Robert Baillie, <a href="http://arxiv.org/abs/0806.4410">Summing the curious series of Kempner and Irwin</a>, arXiv:0806.4410 [math.CA], 2008-2013. [From _Robert G. Wilson v_, Jun 01 2009]
%H A082835 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KempnerSeries.html">Kempner Series</a>.
%H A082835 Wikipedia, <a href="http://en.wikipedia.org/wiki/Kempner_series">Kempner series</a>. [From _M. F. Hasler_, Jan 13 2020]
%H A082835 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 A082835 Equals Sum_{k in A052414\{0}} 1/k, where A052414 = numbers with no digit 6. - _M. F. Hasler_, Jan 15 2020
%e A082835 22.20559815955609188416738048000752710519385610666846327027693823... - _Robert G. Wilson v_, Jun 01 2009
%t A082835 (* see the Mmca in Wolfram Library Archive. - _Robert G. Wilson v_, Jun 01 2009 *)
%Y A082835 Cf. A002387, A024101, A052414 (numbers with no '6'), A011536 (numbers with a '6').
%Y A082835 Cf. A082830, A082831, A082832, A082833, A082834, A082836, A082837, A082838, A082839 (analog for digits 1, 2, 4, ..., 9 and 0).
%K A082835 nonn,cons,base
%O A082835 2,1
%A A082835 _Robert G. Wilson v_, Apr 14 2003
%E A082835 Minor edits by _M. F. Hasler_, Jan 13 2020