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 A082832 #24 Feb 16 2025 08:32:49
%S A082832 2,0,5,6,9,8,7,7,9,5,0,9,6,1,2,3,0,3,7,1,0,7,5,2,1,7,4,1,9,0,5,3,1,1,
%T A082832 1,4,1,4,1,5,3,8,6,9,6,7,4,7,3,0,7,8,3,4,8,9,5,0,8,5,2,8,5,0,0,2,6,7,
%U A082832 2,9,4,9,9,6,1,9,3,8,0,3,5,0,0,5,9,0,4,7,4,9,4,0,8,0,6,0,3,5,3,4,9,8,7,9,0
%N A082832 Decimal expansion of Sum_{k >= 1, k has no digit 3 in base 10} 1/k.
%C A082832 Numbers with a digit 3 (A011533) have asymptotic density 1, i.e., 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 A082832 Julian Havil, Gamma, Exploring Euler's Constant, Princeton University Press, Princeton and Oxford, 2003, page 34.
%H A082832 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 A082832 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 A082832 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KempnerSeries.html">Kempner Series</a>.
%H A082832 Wikipedia, <a href="http://en.wikipedia.org/wiki/Kempner_series">Kempner series</a>. [From _M. F. Hasler_, Jan 13 2020]
%H A082832 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 A082832 Equals Sum_{k in A052405\{0}} 1/k, where A052405 = numbers with no digit 3. - _M. F. Hasler_, Jan 15 2020
%e A082832 20.569877950961230371075217419053111414153869674730783489508528500... - _Robert G. Wilson v_, Jun 01 2009
%t A082832 (* see the Mmca in Wolfram Library Archive. - _Robert G. Wilson v_, Jun 01 2009 *)
%Y A082832 Cf. A002387, A024101, A052405 (numbers with no '3'), A011533 (numbers with '3').
%Y A082832 Cf. A082830, A082831, A082833, A082834, A082835, A082836, A082837, A082838, A082839 (analog for digits 1, 2, 4, ..., 9 and 0).
%K A082832 nonn,cons,base
%O A082832 2,1
%A A082832 _Robert G. Wilson v_, Apr 14 2003
%E A082832 More terms from _Robert G. Wilson v_, Jun 01 2009