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 A082838 #35 Feb 16 2025 08:32:49
%S A082838 2,2,9,2,0,6,7,6,6,1,9,2,6,4,1,5,0,3,4,8,1,6,3,6,5,7,0,9,4,3,7,5,9,3,
%T A082838 1,9,1,4,9,4,4,7,6,2,4,3,6,9,9,8,4,8,1,5,6,8,5,4,1,9,9,8,3,5,6,5,7,2,
%U A082838 1,5,6,3,3,8,1,8,9,9,1,1,1,2,9,4,4,5,6,2,6,0,3,7,4,4,8,2,0,1,8,9,8,9,9,0,9
%N A082838 Decimal expansion of Kempner series Sum_{k>=1, k has no digit 9 in base 10} 1/k.
%C A082838 Numbers with a digit 9 (A011539) 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 A082838 Julian Havil, Gamma, Exploring Euler's Constant, Princeton University Press, Princeton and Oxford, 2003, page 34.
%H A082838 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 A082838 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.
%H A082838 Aubrey J. Kempner, <a href="http://dx.doi.org/10.2307/2972074">A Curious Convergent Series</a>, American Mathematical Monthly, volume 21, number 2, February 1914, pages 48-50. Or <a href="https://www.jstor.org/stable/2972074">JSTOR</a>.
%H A082838 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KempnerSeries.html">Kempner Series</a>.
%H A082838 Wikipedia, <a href="http://en.wikipedia.org/wiki/Kempner_series">Kempner series</a>
%H A082838 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>
%F A082838 Equals Sum_{k in A007095\{0}} 1/k, where A007095 = numbers with no digit 9. - _M. F. Hasler_, Jan 15 2020
%e A082838 22.920676619264150348163657094375931914944762436998481568541998356... - _Robert G. Wilson v_, Jun 01 2009
%t A082838 (* see the Mmca in Wolfram Library Archive link *)
%Y A082838 Cf. A002387, A007095 (numbers with no '9'), A011539 (numbers with a '9'), A024101.
%Y A082838 Cf. A082830 .. A082839 (analog for digits 1, ..., 8 and 0), A140502.
%K A082838 nonn,cons,base
%O A082838 2,1
%A A082838 _Robert G. Wilson v_, Apr 14 2003
%E A082838 More terms from _Robert G. Wilson v_, Apr 14 2009
%E A082838 More terms from _Robert G. Wilson v_, Jun 01 2009
%E A082838 Minor edits by _M. F. Hasler_, Jan 13 2020