|
%I #11 Jan 22 2020 05:15:49
%S 5,6,7,8,10,11,12,13,14,15,16,18,20,21,22,23,24,25,26,27,28,29,30,31,
%T 32,34,36,38,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,
%U 59,60,61,62,63,64,66,68,70,72,74,76,78,80,81
%N Unique monotone sequence satisfying a(a(a(a(n)))) = 2n.
%C For all k >= 0, there is a unique sequence satisfying a^(k+1)=2n. The first differences are 1^k, 2^1, 1^2k, 2^2, 1^4k, 2^4, 1^8k, ...
%H H.-K. Hwang, S. Janson, T.-H. Tsai. <a href="http://algo.stat.sinica.edu.tw/hk/wp-content/files/2016/12/aat-hhrr-1.pdf">Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2)) + f(ceiling(n/2)) + g(n): theory and applications</a>. Preprint, 2016.
%H H.-K. Hwang, S. Janson, T.-H. Tsai. <a href="http://doi.org/10.1145/3127585">Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications</a>. ACM Transactions on Algorithms, 13:4 (2017), #47. DOI:10.1145/3127585.
%F First differences are 1^3, 2^1, 1^6, 2^2, 1^12, 2^4, 1^24, 2^8, ...
%Y Cf. A007378, A003605, A088720.
%K easy,nonn
%O 4,1
%A _Colin Mallows_, Oct 12 2003
|
