cp's OEIS Frontend

A362149 Decimal expansion of K, a constant arising in the analysis of the binary Euclidean algorithm.

%I A362149 #15 May 13 2023 13:55:07
%S A362149 7,0,5,9,7,1,2,4,6,1,0,1,9,1,6,3,9,1,5,2,9,3,1,4,1,3,5,8,5,2,8,8,1,7,
%T A362149 6,6,6,6,7,7
%N A362149 Decimal expansion of K, a constant arising in the analysis of the binary Euclidean algorithm.
%C A362149 Corresponds to the 2/b constant reported in Knuth (1998), p. 352.
%C A362149 Vallée (1998) conjectured that this constant times A362150 equals 4*log(2)/Pi^2; Brent (1999) supported the conjecture with numerical computations and Morris (2016) proved the conjecture.
%D A362149 Richard P. Brent, Further analysis of the binary Euclidean algorithm, Programming Research Group technical report TR-7-99, Oxford University (1999) (see also the arXiv link).
%D A362149 Steven R. Finch, Mathematical Constants, Cambridge University Press, New York, NY, 2003, p. 158.
%D A362149 Donald E. Knuth, The Art of Computer Programming, Vol. 2: Seminumerical Algorithms, 3rd edition, Addison-Wesley, 1998, Sect. 4.5.2, pp. 348-353.
%H A362149 Richard P. Brent, <a href="https://doi.org/10.48550/arXiv.1303.2772">Further analysis of the binary Euclidean algorithm</a>, arXiv:1303.2772 [cs.DS], 1999, p. 12.
%H A362149 Ian D. Morris, <a href="https://doi.org/10.1016/j.aim.2015.12.008">A rigorous version of R. P. Brent's model for the binary Euclidean algorithm</a>, Advances in Mathematics, Vol. 290, 26 Feb. 2016, pp. 73-143.
%H A362149 Brigitte Vallée, <a href="https://doi.org/10.1007/PL00009246">Dynamics of the Binary Euclidean Algorithm: Functional Analysis and Operators</a>, Algorithmica 22 (1998), pp. 660-685.
%H A362149 Wikipedia, <a href="https://en.wikipedia.org/wiki/Binary_GCD_algorithm">Binary GCD algorithm</a>.
%F A362149 Equals (4*log(2)/Pi^2)/A362150 = 4*A118858/A362150.
%e A362149 0.7059712461019163915293141358528817666677...
%Y A362149 Cf. A118858, A345987, A362150.
%K A362149 nonn,cons,hard,more
%O A362149 0,1
%A A362149 _Paolo Xausa_, Apr 09 2023