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A082831 Decimal expansion of Sum_{k >= 1, k has no digit 2 in base 10} 1/k.

%I A082831 #26 Jan 15 2020 14:49:13
%S A082831 1,9,2,5,7,3,5,6,5,3,2,8,0,8,0,7,2,2,2,4,5,3,2,7,7,6,7,7,0,1,9,4,4,5,
%T A082831 4,1,1,5,5,2,6,0,5,3,8,3,1,1,5,4,8,7,0,1,4,9,8,6,8,3,6,2,9,4,9,1,0,4,
%U A082831 3,0,9,0,1,6,0,1,9,5,5,1,8,0,9,2,8,0,5,4,6,2,2,1,1,2,8,4,4,2,8,6,3,5,5,6,5
%N A082831 Decimal expansion of Sum_{k >= 1, k has no digit 2 in base 10} 1/k.
%C A082831 Such sums are called Kempner series, see A082839 (analog for digit 0) for more information. - _M. F. Hasler_, Jan 13 2020
%D A082831 Julian Havil, Gamma, Exploring Euler's Constant, Princeton University Press, Princeton and Oxford, 2003, page 34.
%H A082831 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 A082831 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 A082831 Wikipedia, <a href="http://en.wikipedia.org/wiki/Kempner_series">Kempner series</a>.
%H A082831 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 A082831 Equals Sum_{k in A052404\{0}} 1/k, where A052404 = numbers with no digit 2: these are omitted in the harmonic series. - _M. F. Hasler_, Jan 13 2020
%e A082831 19.25735653280807222453277677019445411552605383115487014986836294...
%t A082831 (* see the Mmca in Wolfram Library Archive *)
%Y A082831 Cf. A002387, A024101, A052404 (numbers with no digit 2).
%Y A082831 Cf. A082830, A082832, A082833, A082834, A082835, A082836, A082837, A082838, A082839 (analog for digits 1, 3, 4, ..., 9 and 0).
%K A082831 nonn,cons,base
%O A082831 2,2
%A A082831 _Robert G. Wilson v_, Apr 14 2003
%E A082831 More terms from _Robert G. Wilson v_, Jun 01 2009