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A345987
Decimal expansion of constant mu(ell) arising in study of complexity of Euclidean algorithm.
3
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, 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, 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
OFFSET
1,2
COMMENTS
The constant is (12/Pi^2)*log(Product_{i>=0} (1+1/2^i)).
REFERENCES
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.
FORMULA
Equals 12*log(QPochhammer(-1,1/2))/Pi^2. - Stefano Spezia, Jul 12 2021
EXAMPLE
1.89919324391088067944828320698125120791994827100906...
MAPLE
evalf(12/Pi^2*log(product(1+1/2^i, i=0..infinity)), 120); # Alois P. Heinz, Jul 12 2021
MATHEMATICA
RealDigits[(12/Pi^2)*Log[Product[1 + 1/2^i, {i, 0, Infinity}]], 10, 105][[1]] (* Amiram Eldar, Jul 12 2021 *)
CROSSREFS
Cf. A081845.
Sequence in context: A010732 A235398 A244959 * A241990 A358519 A256923
KEYWORD
nonn,cons
AUTHOR
N. J. A. Sloane, Jul 12 2021
STATUS
approved