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 A375805 #61 Feb 16 2025 08:34:07
%S A375805 2,6,2,8,3,3,2,8,2,0,4,8,8,1,4,2,0,7,6,9,9,4,0,1,5,1,6,8,7,4,4,4,2,2,
%T A375805 2,9,2,4,1,8,8,7,9,8,0,9,2,5
%N A375805 Decimal expansion of Sum_{n >= 1} 1/A171397(n).
%C A375805 A variation on the harmonic series, in which the denominators are treated as base 11 numbers. Equivalently: sum of reciprocals of positive integers whose base-11 representation contains no digit A (no "10" digit).
%C A375805 Values were calculated using Mathematica code from Baillie & Schmelzer (see link). Note that the code in the Wolfram Library Archive, as it stands, does not support digits > 9 in bases > 10 (and doing the "obvious" thing will be interpreted as asking a different question with a different answer); the code was modified to support this.
%C A375805 Kempner (1914) showed that this series converges. - _N. J. A. Sloane_, Aug 31 2024
%C A375805 There is a slight ambiguity when we get to 1/10. This is to be regarded as 1/(1*11 + 0*1) = (1/11)-in-base-10 and not as 1/A = 1/(10*1) = (1/10)-in-base-10. - _N. J. A. Sloane_, Aug 30 2024
%D A375805 Burnol, Jean-François. "Moments in the exact summation of the curious series of Kempner type." arXiv preprint arXiv:2402.08525 (2024).
%D A375805 A. J. Kempner, A Curious Convergent Series, American Mathematical Monthly, 21 (February, 1914), pp. 48-50. (https://dx.doi.org/10.2307/2972074)
%D A375805 Schmelzer, Thomas, and Robert Baillie. "Summing a curious, slowly convergent series." The American Mathematical Monthly 115.6 (2008): 525-540.
%H A375805 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 A375805 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 A375805 Robert Baillie & Thomas Schmelzer, <a href="https://library.wolfram.com/infocenter/MathSource/7166/">Summing Kempner's Curious (Slowly-Convergent) Series</a>, Wolfram Library Archive
%H A375805 G. W. Brewster, <a href="https://www.jstor.org/stable/3610047">An Old Result in a New Dress</a>, The Mathematical Gazette, Vol. 37, No. 322 (Dec., 1953), pp. 269-270.
%H A375805 John D. Cook, <a href="https://www.johndcook.com/blog/2024/08/29/strange-harmonic-series/">A strange take on the harmonic series</a>, Blog, 29 August 2024.
%H A375805 N. J. A. Sloane, <a href="https://www.youtube.com/watch?v=3RAYoaKMckM">A Nasty Surprise in a Sequence and Other OEIS Stories</a>, Experimental Mathematics Seminar, Rutgers University, Oct 10 2024, Youtube video; <a href="https://sites.math.rutgers.edu/~zeilberg/expmath/sloane85BD.pdf">Slides</a> [Mentions this sequence]
%H A375805 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KempnerSeries.html">Kempner Series</a>.
%H A375805 Wikipedia, <a href="http://en.wikipedia.org/wiki/Kempner_series">Kempner series</a>. [From _M. F. Hasler_, Jan 13 2020]
%e A375805 26.2833282048814207699401516874442229241887980925...
%Y A375805 Cf. A171397, A375523/A375524.
%Y A375805 See also A082830, A082831, A082832, A082833, A082834, A082835, A082836, A082837, A082838, A082839.
%K A375805 nonn,cons,base,more
%O A375805 2,1
%A A375805 _Robert C. Lyons_, Aug 29 2024
%E A375805 Corrected data provided by _Gareth McCaughan_, Sep 02 2024