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Decimal expansion of Sum_{k >= 1, 3|floor(k*log_10(2))} 1/3^k.
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%I #16 May 20 2024 02:09:07

%S 4,8,1,5,0,6,5,7,0,9,2,5,3,4,8,8,6,8,7,1,6,9,7,6,0,1,9,5,0,9,5,5,1,5,

%T 5,1,2,8,0,3,1,4,3,2,0,5,5,2,6,9,8,7,6,2,1,7,2,2,8,9,7,5,5,4,8,6,7,9,

%U 3,6,9,2,2,0,4,9,0,1,1,6,9,0,4,2,4,1,0,9,9,9

%N Decimal expansion of Sum_{k >= 1, 3|floor(k*log_10(2))} 1/3^k.

%H Paolo Xausa, <a href="/A372805/b372805.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 3554/7381, correct to 49 digits: see Example 4.2 (d) in Borwein and Borwein (1992), p. 635.

%e 0.481506570925348868716976019509551551280314320552698762172...

%t First[RealDigits[Sum[If[Divisible[Floor[k*Log10[2]], 3], 1/3^k, 0], {k, 250}], 10, 100]]

%Y Cf. A000244.

%K nonn,cons

%O 0,1

%A _Paolo Xausa_, May 13 2024