Search: id:A082839
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%I A082839
%S A082839 2,3,1,0,3,4,4,7,9,0,9,4,2,0,5,4,1,6,1,6,0,3,4,0,5,4,0,4,3,3,2,5,5,9,8,
%T A082839 1,3,8,3,0,2,8,0,0,0,0,5,2,8,2,1,4,1,8,8,6,7,2,3,0,9,4,7,7,2,7,3,8,7,5,
%U A082839 0,7,9,6,0,6,1,4,1,9,4,2,6,3,5,9,2,0,1,9,1,0,5,2,6,1,3,9,3,3,8,6,5,2,1
%N A082839 Decimal expansion of the (finite) value of the sum_{ k >= 1, k has no 
               zero digit in base 10 } 1/k.
%C A082839 "The most novel culling of the terms of the harmonic series has to be 
               due to A. J. Kempner, who in 1914 considered what would happen if 
               all terms are removed from it which have a particular digit appearing 
               in their denominators. For example, if we choose the digits 7, we 
               would exclude the terms with denominators such as 7, 27, 173,33779, 
               etc. There are 10 such series, each resulting from the removal of 
               one of the digits 0, 1, 2, ..., 9 and the first question which naturally 
               arises is just what percentage of the terms of the series are we 
               removing by the process?"
%C A082839 "The sum of the reciprocals, 1 + 1/2 + 1/3 + 1/4 + 1/5 + ... [A002387] 
               is unbounded. By taking sufficiently many terms, it can be made as 
               large as one pleases. However, if the reciprocals of all numbers 
               that when written in base 10 contain at least one 0 are omitted, 
               then the sum has the limit, 23.10345... [Boas and Wrench, AMM v78]." 
               - Wells.
%D A082839 Robert Baillie, Sums of reciprocals of integers missing a given digit, 
               Amer. Math. Monthly, 86 (1979), 372-374.
%D A082839 Julian Havil, Gamma, Exploring Euler's Constant, Princeton University 
               Press, Princeton and Oxford, 2003, page 34.
%D A082839 A. D. Wadhwa, Some convergent subseries of the harmonic series, Amer. 
               Math. Monthly, 85 (1978), 661-663.
%D A082839 David Wells, "The Penguin Dictionary of Curious and Interesting Numbers,
               " Revised Edition, Penguin Books, London, England, 1997.
%H A082839 Baillie, Revised August 17, 2008, <a href="http://arxiv.org/ftp/arxiv/
               papers/0806/0806.4410.pdf"> Summing The Curious Series Of Kempner 
               And Irwin</a> [From Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 01 
               2009]
%H A082839 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 (rgwv(AT)rgwv.com), Jun 01 2009]
%e A082839 23.10344790942054161603...
%e A082839 = 23.10344790942054161603405404332559813830280000528214188672309477... 
               [From Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 01 2009]
%t A082839 (* see the Mmca in Wolfram Library Archive *) [From Robert G. Wilson 
               v (rgwv(AT)rgwv.com), Jun 01 2009]
%Y A082839 Cf. A002387, A052386, A082830, A082831, A082832, A082833, A082834, A082835, 
               A082836, A082837, A082838.
%Y A082839 Sequence in context: A154720 A071501 A004572 this_sequence A130717 A137396 
               A167666
%Y A082839 Adjacent sequences: A082836 A082837 A082838 this_sequence A082840 A082841 
               A082842
%K A082839 nonn,cons,base
%O A082839 2,1
%A A082839 Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 14 2003
%E A082839 More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 01 2009

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