A345987 - OEIS

%I #14 Jul 12 2021 14:55:05

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

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

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

%N Decimal expansion of constant mu(ell) arising in study of complexity of Euclidean algorithm.

%C The constant is (12/Pi^2)*log(Product_{i>=0} (1+1/2^i)).

%D Lhote, Loïck, and Brigitte Vallée. "Sharp estimates for the main parameters of the Euclid Algorithm." In Latin American Symposium on Theoretical Informatics, pp. 689-702. Springer, Berlin, Heidelberg, 2006.

%F Equals 12*log(QPochhammer(-1,1/2))/Pi^2. - _Stefano Spezia_, Jul 12 2021

%e 1.89919324391088067944828320698125120791994827100906...

%p evalf(12/Pi^2*log(product(1+1/2^i, i=0..infinity)), 120);  # _Alois P. Heinz_, Jul 12 2021

%t RealDigits[(12/Pi^2)*Log[Product[1 + 1/2^i, {i, 0, Infinity}]], 10, 105][[1]] (* _Amiram Eldar_, Jul 12 2021 *)

%Y Cf. A081845.

%K nonn,cons

%O 1,2

%A _N. J. A. Sloane_, Jul 12 2021