A246765 Decimal expansion of a limit associated with the asymptotic number of ways of writing a number as a sum of powers of 2, with each power used at most twice (cardinality of "alternating bit sets" of a given number, also known as Stern's diatomic sequence).

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

Offset

0,1

Comments

See A002487.

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.16.3 Alternating bit sets, p. 148.

Links

Table of n, a(n) for n=0..102.

Neil J. Calkin and Herbert S. Wilf, Binary Partitions of Integers and Stern-Brocot-Like Trees, 1998. Section 10, open question 9 (which is answered by Coons and Tyler).

Michael Coons and Jason Tyler, The maximal order of Stern's diatomic sequence. arXiv:1307.1521 [math.NT], 2013-2014.

Steven R. Finch, Errata and Addenda to Mathematical Constants, arXiv:2001.00578 [math.HO], 2020. See p. 20.

Formula

3^(log(phi)/log(2))/sqrt(5), where phi is the golden ratio.

Example

0.95885419082476738320909430420365929574868299100585691491...

Mathematica

RealDigits[ 3^(Log[GoldenRatio]/Log[2]) / Sqrt[5], 10, 103] // First

Crossrefs

Cf. A002487.

Sequence in context: A146483 A090463 A272795 * A191759 A289505 A371528

Adjacent sequences: A246762 A246763 A246764 * A246766 A246767 A246768

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Sep 03 2014

Status

approved