

A179951


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


2



1, 5, 2, 8, 9, 9, 9, 5, 6, 0, 6, 9, 6, 8, 8, 8, 4, 1, 8, 3, 8, 2, 6, 3, 9, 4, 9, 4, 5, 1, 0, 9, 9, 6, 9, 6, 5, 1, 1, 5, 3, 9, 3, 9, 9, 7, 7, 1, 5, 0, 5, 1, 2, 5, 3, 1, 3, 2, 4, 7, 5, 9, 2, 0, 5, 3, 1, 7, 5, 1, 3, 5, 9, 5, 3, 2, 0, 1, 4, 1, 7, 0, 1, 2, 3, 8, 0, 8, 8, 6, 4, 3, 0, 5, 7, 0, 7, 9, 7, 0, 2, 2, 2, 7, 0
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OFFSET

1,2


COMMENTS

Obviously for k > 0 in base 2 having no bit equal to 1 the sum is 0 and for 1 bit equal to 1 the sum is 2.


LINKS

Table of n, a(n) for n=1..105.
Robert Baillie, Summing The Curious Series Of Kempner and Irwin, arXiv:0806.4410 [math.CA], 20082015.
Wolfram Library Archive, KempnerSums.nb (8.6 KB)  Mathematica Notebook, Summing Kempner's Curious (SlowlyConvergent) Series


FORMULA

Equals Sum_{j>=1} Sum_{i=0..j1} 1/(2^i + 2^j).
From Amiram Eldar, Jun 30 2020: (Start)
Equals Sum_{k>=0} 1/(2^k + 1/2).
Equals 2 * A323482  1. (End)


EXAMPLE

Sum_{k>0} 1/A018900(k) = 1.52899956069688841838263949451...


MATHEMATICA

(* first install irwinSums.m, see either reference, then *) First@ RealDigits@ iSum[1, 2, 2^7, 2]


CROSSREFS

Cf. A065442, A082830, A082831, A082832, A082833, A082834, A082835, A082836, A082837, A082838, A082839, A140502, A160502, A018900, A323482.
Sequence in context: A200135 A001062 A187876 * A198192 A046878 A078335
Adjacent sequences: A179948 A179949 A179950 * A179952 A179953 A179954


KEYWORD

base,cons,nonn


AUTHOR

Robert G. Wilson v, Aug 03 2010


STATUS

approved



