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A362149
Decimal expansion of K, a constant arising in the analysis of the binary Euclidean algorithm.
2
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, 6, 6, 6, 6, 7, 7
OFFSET
0,1
COMMENTS
Corresponds to the 2/b constant reported in Knuth (1998), p. 352.
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.
REFERENCES
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).
Steven R. Finch, Mathematical Constants, Cambridge University Press, New York, NY, 2003, p. 158.
Donald E. Knuth, The Art of Computer Programming, Vol. 2: Seminumerical Algorithms, 3rd edition, Addison-Wesley, 1998, Sect. 4.5.2, pp. 348-353.
LINKS
Richard P. Brent, Further analysis of the binary Euclidean algorithm, arXiv:1303.2772 [cs.DS], 1999, p. 12.
Ian D. Morris, A rigorous version of R. P. Brent's model for the binary Euclidean algorithm, Advances in Mathematics, Vol. 290, 26 Feb. 2016, pp. 73-143.
Brigitte Vallée, Dynamics of the Binary Euclidean Algorithm: Functional Analysis and Operators, Algorithmica 22 (1998), pp. 660-685.
FORMULA
Equals (4*log(2)/Pi^2)/A362150 = 4*A118858/A362150.
EXAMPLE
0.7059712461019163915293141358528817666677...
CROSSREFS
KEYWORD
nonn,cons,hard,more
AUTHOR
Paolo Xausa, Apr 09 2023
STATUS
approved