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Decimal expansion of Sum_{k >= 1} A210436(k)^2/2^k.
1

%I #10 May 20 2024 02:09:03

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

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

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

%N Decimal expansion of Sum_{k >= 1} A210436(k)^2/2^k.

%H Paolo Xausa, <a href="/A372925/b372925.txt">Table of n, a(n) for n = 1..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 196669/37303, correct to 88 digits: see Example 4.2 (c) in Borwein and Borwein (1992), pp. 634-635, although there is a typo in the denominator of the summands (6^k instead of 2^k).

%e 5.2722033080449293622496850119293354421896362222877516553628...

%t First[RealDigits[Sum[IntegerLength[6^k]^2/2^k, {k, 350}], 10, 100]]

%Y Cf. A000079, A000400, A210436, A372804.

%K nonn,cons

%O 1,1

%A _Paolo Xausa_, May 17 2024