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
Examples
0.95885419082476738320909430420365929574868299100585691491...
References
- Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.16.3 Alternating bit sets, p. 148.
Links
- 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.
Crossrefs
Cf. A002487.
Programs
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Mathematica
RealDigits[ 3^(Log[GoldenRatio]/Log[2]) / Sqrt[5], 10, 103] // First
Formula
3^(log(phi)/log(2))/sqrt(5), where phi is the golden ratio.
Comments