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Decimal expansion of Sum_{k >= 1, A034887(k) even} 1/2^k.
2

%I #12 May 20 2024 03:01:29

%S 1,1,1,2,1,9,5,1,2,1,9,5,1,2,1,9,5,1,2,1,9,5,1,2,1,9,5,1,2,2,0,4,9,7,

%T 3,0,9,2,2,7,9,8,3,3,1,2,3,0,3,3,4,3,4,2,6,8,9,1,3,7,9,4,3,8,2,9,8,8,

%U 2,3,5,9,1,3,9,7,7,2,6,2,4,1,7,4,7,8,6,6,4,2

%N Decimal expansion of Sum_{k >= 1, A034887(k) even} 1/2^k.

%H Paolo Xausa, <a href="/A372804/b372804.txt">Table of n, a(n) for n = 0..10000</a>

%H J. M. Borwein and P. B. Borwein, <a href="https://doi.org/10.2307/2324993">Strange Series and High Precision Fraud</a>, The American Mathematical Monthly, Vol. 99, No. 7 (1992), pp. 622-640.

%F Approximately 114/1025, correct to 30 digits: see Example 4.2 (b) in Borwein and Borwein (1992), p. 634.

%e 0.1112195121951219512195121951220497309227983312303343426891...

%t First[RealDigits[Sum[If[OddQ[IntegerLength[2^k]], 0, 1/2^k], {k, 350}], 10, 100]]

%Y Cf. A000079, A034887.

%K nonn,cons

%O 0,4

%A _Paolo Xausa_, May 13 2024