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Decimal expansion of Sum_{k >= 1} floor((Pi/2)*k)/2^k.
3

%I #14 May 20 2024 10:30:53

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

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

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

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

%H Paolo Xausa, <a href="/A372610/b372610.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 339/127, correct to 67 digits: see Example 4.1 (a) in Borwein and Borwein (1992), p. 633.

%e 2.669291338582677165354330708661417322834645669291338582677...

%t First[RealDigits[Sum[Floor[Pi*k/2]/2^k, {k, 400}], 10, 100]]

%Y Cf. A000796, A019669, A140758.

%K nonn,cons

%O 1,1

%A _Paolo Xausa_, May 07 2024