cp's OEIS Frontend

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).

%I A246765 #21 May 08 2020 16:13:35
%S A246765 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,
%T A246765 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,
%U A246765 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
%N 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).
%C A246765 See A002487.
%D A246765 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.16.3 Alternating bit sets, p. 148.
%H A246765 Neil J. Calkin and Herbert S. Wilf, <a href="http://www.math.clemson.edu/~calkin/Papers/test-bak.pdf">Binary Partitions of Integers and Stern-Brocot-Like Trees</a>, 1998.  Section 10, open question 9 (which is answered by Coons and Tyler).
%H A246765 Michael Coons and Jason Tyler, <a href="http://arxiv.org/abs/1307.1521">The maximal order of Stern's diatomic sequence.</a> arXiv:1307.1521 [math.NT], 2013-2014.
%H A246765 Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, arXiv:2001.00578 [math.HO], 2020. See p. 20.
%F A246765 3^(log(phi)/log(2))/sqrt(5), where phi is the golden ratio.
%e A246765 0.95885419082476738320909430420365929574868299100585691491...
%t A246765 RealDigits[ 3^(Log[GoldenRatio]/Log[2]) / Sqrt[5], 10, 103] // First
%Y A246765 Cf. A002487.
%K A246765 nonn,cons,easy
%O A246765 0,1
%A A246765 _Jean-François Alcover_, Sep 03 2014