A115836 Self-describing sequence. The n-th integer of the sequence indicates how many integers of the sequence are strictly < 2n.

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, 36, 38, 40, 42, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 95, 96, 97, 98, 99, 100, 101

Offset

1,2

Comments

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.

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

Links

Table of n, a(n) for n=1..70.

Hsien-Kuei Hwang, S. Janson, and T.-H. Tsai, Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2)) + f(ceiling(n/2)) + g(n): theory and applications, Preprint, 2016.

Hsien-Kuei Hwang, S. Janson, and T.-H. Tsai, Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications, ACM Transactions on Algorithms, 13:4 (2017), #47; DOI: 10.1145/3127585.

Formula

a(n) = A007378(n+1) - 2. - Benoit Cloitre, May 22 2008

Example

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)

Crossrefs

Cf. A007378, A080653.

Sequence in context: A342495 A035500 A080653 * A176554 A366322 A284895

Adjacent sequences: A115833 A115834 A115835 * A115837 A115838 A115839

Keyword

easy,nonn

Author

Eric Angelini, Feb 01 2006

Status

approved