cp's OEIS Frontend

A367110 Decimal expansion of Sum_{k has exactly 3 bits equal to 1 in base 2} 1/k.

%I A367110 #32 Dec 21 2023 11:19:19
%S A367110 1,4,2,8,5,9,1,5,4,5,8,5,2,6,3,8,1,2,3,9,9,6,8,5,4,8,4,4,4,0,0,5,3,7,
%T A367110 9,5,2,7,8,1,6,8,8,7,5,0,9,0,6,1,3,3,0,6,8,3,9,7,1,8,9,5,2,9,7,7,5,3,
%U A367110 6,5,9,5,0,0,3,9,7,4,4,5,2,9,6,8,0,0,5,1,1,6,3,5,7,0,8,6,2,2,7,2,7,1,9,1,5
%N A367110 Decimal expansion of Sum_{k has exactly 3 bits equal to 1 in base 2} 1/k.
%C A367110 For 1 bit equal to 1 the sum is 2, for 2 bits equal to 1 the sum is 1.52899956069688841838263949451... (see A179951).
%H A367110 Robert Baillie, <a href="https://arxiv.org/abs/0806.4410">Summing The Curious Series Of Kempner and Irwin</a>, arXiv:0806.4410 [math.CA], 2008-2015.
%H A367110 Wolfram Library Archive, KempnerSums.nb (8.6 KB) - Mathematica Notebook, <a href="https://library.wolfram.com/infocenter/MathSource/7166/">Summing Kempner's Curious (Slowly-Convergent) Series</a>
%F A367110 Equals Sum_{m>=2} Sum_{j=1..m-1} Sum_{i=0..j-1} 1/(2^i + 2^j + 2^m).
%F A367110 Equals 2 * Sum_{j>=2} Sum_{i=1..j-1} 1/(2^i + 2^j + 1).
%F A367110 Equals Sum_{k>=1} 1/A014311(k).
%e A367110 1.4285915458526381...
%t A367110 RealDigits[iSum[1, 3, 105, 2]][[1]] (* _Amiram Eldar_, Dec 16 2023, using Baillie's irwinSums.m *)
%Y A367110 Cf. A179951, A014311.
%K A367110 cons,nonn,base
%O A367110 1,2
%A A367110 _Tengiz Gogoberidze_, Dec 16 2023