A390489 Decimal expansion of log_2(1 + 1/3).

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

Offset

0,1

Comments

Frequency of the term 1 in the continued fraction expansion of almost all real numbers x. See Singh.

Links

Table of n, a(n) for n=0..99.

R. Kuzmin, Sur un problème de Gauss, in Atti del Congresso Internazionale dei Matematici, Bologna, 1928, pp. 83-90.

Shreyas Singh, Zhuo Zhang, and AJ Hildebrand, An Elementary Characterization of the Gauss-Kuzmin Measure in the Theory of Continued Fractions, arXiv:2511.01992 [math.NT], 2025. See p. 3.

Index entries for transcendental numbers.

Formula

Equals 2 - log_2(3) = 2 - A020857.

Example

0.4150374992788438185462610560521834912401855923...

Mathematica

RealDigits[2-Log2[3], 10, 100][[1]]

Crossrefs

Cf. A020857, A390492.

Sequence in context: A303144 A370451 A394912 * A397552 A265602 A185373

Adjacent sequences: A390486 A390487 A390488 * A390490 A390491 A390492

Keyword

nonn,cons

Author

Stefano Spezia, Nov 07 2025

Status

approved