OFFSET
1,2
COMMENTS
For 1 bit equal to 1 the sum is 2, for 2 bits equal to 1 the sum is 1.52899956069688841838263949451... (see A179951).
LINKS
Robert Baillie, Summing The Curious Series Of Kempner and Irwin, arXiv:0806.4410 [math.CA], 2008-2015.
Wolfram Library Archive, KempnerSums.nb (8.6 KB) - Mathematica Notebook, Summing Kempner's Curious (Slowly-Convergent) Series
FORMULA
Equals Sum_{m>=2} Sum_{j=1..m-1} Sum_{i=0..j-1} 1/(2^i + 2^j + 2^m).
Equals 2 * Sum_{j>=2} Sum_{i=1..j-1} 1/(2^i + 2^j + 1).
Equals Sum_{k>=1} 1/A014311(k).
EXAMPLE
1.4285915458526381...
MATHEMATICA
RealDigits[iSum[1, 3, 105, 2]][[1]] (* Amiram Eldar, Dec 16 2023, using Baillie's irwinSums.m *)
CROSSREFS
KEYWORD
AUTHOR
Tengiz Gogoberidze, Dec 16 2023
STATUS
approved