A345987 Decimal expansion of constant mu(ell) arising in study of complexity of Euclidean algorithm.

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.

Links

Table of n, a(n) for n=1..104.

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

Adjacent sequences: A345984 A345985 A345986 * A345988 A345989 A345990

Keyword

nonn,cons

Author

N. J. A. Sloane, Jul 12 2021

Status

approved