%I #18 Jun 30 2024 22:50:21

%S 1,2,4,5,6,8,10,11,12,13,14,16,18,20,22,23,24,25,26,27,28,29,30,32,34,

%T 36,38,40,42,44,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,64,

%U 66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,95,96,97,98,99,100,101

%N Self-describing sequence. The n-th integer of the sequence indicates how many integers of the sequence are strictly < 2n.

%C Terms computed by Gilles Sadowski. In building step by step the sequence one has sometimes the choice for an integer. If so take the smallest available one.

%C {a(n)} is the lexicographically earliest monotonic sequence of positive integers satisfying a(a(n)+1) = 2*n. - _Yifan Xie_, Jun 25 2024

%H Hsien-Kuei Hwang, S. Janson, and T.-H. Tsai, <a href="http://140.109.74.92/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 Hsien-Kuei Hwang, S. Janson, and T.-H. Tsai, <a href="https://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 a(n) = A007378(n+1) - 2. - _Benoit Cloitre_, May 22 2008

%e a(7)=10 because there are 10 integers in the sequence which are strictly < 14 (they are 1,2,4,5,6,8,10,11,12,13)

%Y Cf. A007378, A080653.

%K easy,nonn

%O 1,2

%A _Eric Angelini_, Feb 01 2006