0.11659102484...
For b = 3..23, the table below lists the minimum and maximum values of the smoothed partial sum S'(j) (see Comments) among values of j such that 1/t(j) is an odd number in the interval [2^b, 2^(b+1)]. (The table begins at b=3 because the first odd denominator in the alternating sum is A024619(5) = 15, which lies in the interval [2^3, 2^4].)
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b min S'(j) (1/t(j) odd) max S'(j) (1/t(j) odd)
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3 0.111904761904761904... 0.111904761904761904...
4 0.115873015873015873... 0.115873015873015873...
5 0.116751763887986798... 0.116780441780441780...
6 0.116515193298484059... 0.116521345165903716...
7 0.116576739754580331... 0.116579123025777238...
8 0.116593064475078642... 0.116593574635271689...
9 0.116589740175207247... 0.116589805144898644...
10 0.116590699983114246... 0.116590715183253815...
11 0.116590952081202610... 0.116590954393007789...
12 0.116591012248587507... 0.116591013407441019...
13 0.116591027701733147... 0.116591027880912807...
14 0.116591024064904443... 0.116591024080256316...
15 0.116591025004372396... 0.116591025007229633...
16 0.116591024772646678... 0.116591024773252190...
17 0.116591024831104914... 0.116591024831253967...
18 0.116591024845789528... 0.116591024845809974...
19 0.116591024842154904... 0.116591024842161473...
20 0.116591024841250054... 0.116591024841250922...
21 0.116591024841022776... 0.116591024841022992...
22 0.116591024840966103... 0.116591024840966133...
23 0.116591024840980341... 0.116591024840980345...
24 0.116591024840976791... 0.116591024840976792...
(End)
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